From 249152409e3b792a190f8e17e1e79fca206d9cf7 Mon Sep 17 00:00:00 2001 From: zhaot4 Date: Tue, 3 Sep 2024 17:54:39 -0400 Subject: [PATCH 1/6] updated three files --- .../Assignment01/zhaot4-f24-assignment1.Rmd | 16 ++- .../Assignment01/zhaot4-f24-assignment1.html | 111 ++++++++++++++++-- .../Assignment01/zhaot4-f24-assignment1.pdf | Bin 297468 -> 297471 bytes 3 files changed, 115 insertions(+), 12 deletions(-) diff --git a/StudentNotebooks/Assignment01/zhaot4-f24-assignment1.Rmd b/StudentNotebooks/Assignment01/zhaot4-f24-assignment1.Rmd index 274fea4..97b62d6 100644 --- a/StudentNotebooks/Assignment01/zhaot4-f24-assignment1.Rmd +++ b/StudentNotebooks/Assignment01/zhaot4-f24-assignment1.Rmd @@ -354,7 +354,21 @@ What do the clustering and PCA results tell us about the data detected by the The clustering and PCA results from the M20 PIXL experiment data reveal a heterogeneous composition in the Martian surface samples, indicating diverse geological processes and materials. The three distinct clusters point to different rock or soil types, suggesting a complex geological history involving various environmental conditions and processes. ```{r} - +library(ggplot2) +library(factoextra) +library(dplyr) +summary(pixl_trim.mat.pca) +loadings <- pixl_trim.mat.pca$rotation +print("PCA Loadings:") +print(loadings) +data <- as.factor(km$cluster) +fviz_pca_biplot(pixl_trim.mat.pca, +geom.ind = "point", +col.ind = data, # Color by clusters +palette = "jco", +addEllipses = FALSE, +label = "var", +title = "PCA Biplot of Martian Geochemical Data") ``` ## SAVE, COMMIT and PUSH YOUR CHANGES! diff --git a/StudentNotebooks/Assignment01/zhaot4-f24-assignment1.html b/StudentNotebooks/Assignment01/zhaot4-f24-assignment1.html index a39bb51..09d77ae 100644 --- a/StudentNotebooks/Assignment01/zhaot4-f24-assignment1.html +++ b/StudentNotebooks/Assignment01/zhaot4-f24-assignment1.html @@ -11,9 +11,9 @@ - + -RPI github and Mars 2020 PIXL Example Notebook: +RPI github and Mars 2020 PIXL-zhaot4 Notebook: + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ + + + + + + + +
+

1 DAR ASSIGNMENT 2 +(Introduction): Introductory DAR Notebook

+

This notebook is broken into two main parts:

+
    +
  • Part 1: Preparing your local repo for +DAR Assignment 2

  • +
  • Part 2: Loading and some analysis of the Mars +2020 (M20) Datasets

    +
      +
    • Lithology: Summarizes the mineral characteristics of samples +collected at certain sample locations.
    • +
    • PIXL: Planetary Instrument for X-ray Lithochemistry. Measures +elemental chemistry of samples at sub-millimeter scales of +samples.
    • +
    • SHERLOC: Scanning Habitable Environments with Raman and Luminescence +for Organics and Chemicals. Uses cameras, a spectrometer, and a +laser of samples to search for organic compounds and minerals that have +been altered in watery environments and may be signs of past microbial +life.
    • +
    • LIBS: Laser-induced breakdown spectroscopy. Uses a laser beam to +help identify minerals in samples and other areas that are beyond the +reach of the rover’s robotic arm or in areas too steep for the rover to +travel.
    • +
  • +
  • Part 3: Individual analysis of your team’s +dataset

  • +
  • Part 4: Preparation of Team +Presentation

  • +
+

NOTE: The RPI github repository for all the code and +data required for this notebook may be found at:

+ +
+
+

2 DAR ASSIGNMENT 2 (Part +1): Preparing your local repo for Assignment 2

+

In this assignment you’ll start by making a copy of the Assignment 2 +template notebook, then you’ll add to your copy with your original work. +The instructions which follow explain how to accomplish this.

+

NOTE: You already cloned the +DAR-Mars-F24 repository for Assignment 1; you do +not need to make another clone of the repo, but you must begin +by updating your copy as instructed below:

+
+

2.1 Updating your local +clone of the DAR-Mars-F24 repository

+
    +
  • Access RStudio Server on the IDEA Cluster at http://lp01.idea.rpi.edu/rstudio-ose/ +
      +
    • REMINDER: You must be on the RPI VPN!!
    • +
  • +
  • Access the Linux shell on the IDEA Cluster by clicking the +Terminal tab of RStudio Server (lower left panel). +
      +
    • You now see the Linux shell on the IDEA Cluster
    • +
    • cd (change directory) to enter your home directory +using: cd ~
    • +
    • Type pwd to confirm where you are
    • +
  • +
  • In the Linux shell, cd to DAR-Mars-F24 +
      +
    • Type git pull origin main to pull any updates
    • +
    • Always do this when you being work; we might have added or changed +something!
    • +
  • +
  • In the Linux shell, cd into Assignment02 +
      +
    • Type ls -al to list the current contents
    • +
    • Don’t be surprised if you see many files!
    • +
  • +
  • In the Linux shell, type git branch to verify your +current working branch +
      +
    • If it is not dar-yourrcs, type +git checkout dar-yourrcs (where yourrcs is +your RCS id)
    • +
    • Re-type git branch to confirm
    • +
  • +
  • Now in the RStudio Server UI, navigate to the +DAR-Mars-F24/StudentNotebooks/Assignment02 directory via +the Files panel (lower right panel) +
      +
    • Under the More menu, set this to be your R working +directory
    • +
    • Setting the correct working directory is essential for interactive R +use!
    • +
  • +
+

You’re now ready to start coding Assignment 2!

+
+
+

2.2 Creating your copy of +the Assignment 2 notebook

+
    +
  1. In RStudio, make a copy of +dar-f24-assignment2-template.Rmd file using a new, +original, descriptive filename that includes your RCS +ID! +
      +
    • Open dar-f24-assignment2-template.Rmd
    • +
    • Save As… using a new filename that includes your +RCS ID
    • +
    • Example filename for user erickj4: +erickj4-assignment2-f24.Rmd
    • +
    • POINTS OFF IF: +
        +
      • You don’t create a new filename!
      • +
      • You don’t include your RCS ID!
      • +
      • You include template in your new filename!
      • +
    • +
  2. +
  3. Edit your new notebook using RStudio and save +
      +
    • Change the title: and subtitle: headers +(at the top of the file)
    • +
    • Change the author:
    • +
    • Don’t bother changing the date:; it should update +automagically…
    • +
    • Save your changes
    • +
  4. +
  5. Use the RStudio Knit command to create an PDF file; +repeat as necessary +
      +
    • Use the down arrow next to the word Knit and select +Knit to PDF
    • +
    • You may also knit to HTML…
    • +
  6. +
  7. In the Linux terminal, use git add to add each new file +you want to add to the repository +
      +
    • Type: git add yourfilename.Rmd
    • +
    • Type: git add yourfilename.pdf (created when you +knitted)
    • +
    • Add your HTML if you also created one…
    • +
  8. +
  9. When you’re ready, in Linux commit your changes: +
      +
    • Type: git commit -m "some comment" where “some comment” +is a useful comment describing your changes
    • +
    • This commits your changes to your local repo, and sets the stage for +your next operation.
    • +
  10. +
  11. Finally, push your commits to the RPI github repo +
      +
    • Type: git push origin dar-yourrcs (where +dar-yourrcs is the branch you’ve been working in)
    • +
    • Your changes are now safely on the RPI github.
    • +
  12. +
  13. REQUIRED: On the RPI github, submit a pull +request. +
      +
    • In a web browser, navigate to https://github.rpi.edu/DataINCITE/DAR-Mars-F24
    • +
    • In the branch selector drop-down (by default says +master), select your branch
    • +
    • Submit a pull request for your branch
    • +
    • One of the DAR instructors will merge your branch, and your new +files will be added to the master branch of the repo. Do not merge +your branch yourself!
    • +
  14. +
+
+
+
+

3 DAR ASSIGNMENT 2 (Part +2): Loading the Mars 2020 (M20) Datasets

+

In this assignment there are four datasets from separate instruments +on the Mars Perserverance rover available for analysis:

+
    +
  • Lithology: Summarizes the mineral characteristics +of samples collected at certain sample locations
  • +
  • PIXL: Planetary Instrument for X-ray Lithochemistry +of collected samples
  • +
  • SHERLOC: Scanning Habitable Environments with Raman +and Luminescence for Organics and Chemicals for collected samples
  • +
  • LIBS: Laser-induced breakdown spectroscopy which +are measured in many areas (not just samples)
  • +
+

Each dataset provides data about the mineralogy of the surface of +Mars. Based on the purpose and nature of the instrument, the data is +collected at different intervals along the path of Perseverance as it +makes it way across the Jezero crater. Some of the data (esp. LIBS) is +collected almost every Martian day, or sol. Some of the data +(PIXL and SHERLOC) is only collected at certain sample locations of +interest

+

Your objective is to perform an analysis of the your team’s assigned +dataset in order to learn all you can about these Mars samples.

+

NOTES:

+
    +
  • All of these datasets can be found in +/academics/MATP-4910-F24/DAR-Mars-F24/Data
  • +
  • We have included a comprehensive samples.Rds dataset +that includes useful details about the sample locations, including +Martian latitude and longitude and the sol that individual samples were +collected.
  • +
  • Also included is rover.waypoints.Rds that provides +detailed location information (lat/lon) for the Perseverance rover +throughout its journey, up to the present. This can be updated when +necessary using the included roverStatus-f24.R script.
  • +
  • A general guide to the available Mars 2020 data is available here: +https://pds-geosciences.wustl.edu/missions/mars2020/index.htm
  • +
  • Other useful MARS 2020 sites https://science.nasa.gov/mission/mars-2020-perseverance/mars-rock-samples/ +and https://an.rsl.wustl.edu/m20/AN/an3.aspx?AspxAutoDetectCookieSupport=1
  • +
  • Note that PIXL, SHERLOC, and Lithology describe 16 sample that were +physically collected. There will eventually be 38 samples. These +datasets can be merged by sample. The LIBS data includes observations +collected at many more locations so how to combine the LIBS data with +the other datasets is an open research question.
  • +
+
+

3.1 Data Set A: Load the +Lithology Data

+

The first five features of the dataset describe twenty-four (24) +rover sample locations.

+

The remaining features provides a simple binary (1 or +0) summary of presence or absence of 35 minerals at the 24 +rover sample locations.

+

Only the first sixteen (16) samples are maintained, as the remaining +are missing the mineral descriptors.

+

The following code “cleans” the dataset to prepare for analysis. It +first creates a dataframe with metadata and measurements for samples, +and then creates a matrix containing only numeric measurements for later +analysis.

+
# Load the saved lithology data with locations added
+lithology.df<- readRDS("/academics/MATP-4910-F24/DAR-Mars-F24/Data/mineral_data_static.Rds")
+
+# Cast samples as numbers
+lithology.df$sample <- as.numeric(lithology.df$sample)
+
+# Convert rest into factors
+lithology.df[sapply(lithology.df, is.character)] <-
+  lapply(lithology.df[sapply(lithology.df, is.character)], 
+                                       as.factor)
+
+# Keep only first 16 samples because the data for the rest of the samples is not available yet
+lithology.df<-lithology.df[1:16,]
+
+# Look at summary of cleaned data frame
+summary(lithology.df)
+
##      sample              name          SampleType         campaign
+##  Min.   : 1.00   Atsah     : 1   atmospheric: 1   Crater Floor:9  
+##  1st Qu.: 4.75   Bearwallow: 1   regolith   : 0   Delta Front :7  
+##  Median : 8.50   Coulettes : 1   rock core  :15   Margin Unit :0  
+##  Mean   : 8.50   Hahonih   : 1                                    
+##  3rd Qu.:12.25   Hazeltop  : 1                                    
+##  Max.   :16.00   Kukaklek  : 1                                    
+##                  (Other)   :10                                    
+##          abrasion feldspar plagioclase pyroxene olivine quartz apatite
+##  Alfalfa     :2   0:14     0:13        0: 5     0: 6    0:14   0:13   
+##  Bellegarde  :2   1: 2     1: 3        1:11     1:10    1: 2   1: 3   
+##  Berry Hollow:2                                                       
+##  Dourbes     :2                                                       
+##  Novarupta   :2                                                       
+##  Quartier    :2                                                       
+##  (Other)     :4                                                       
+##  FeTi_Oxides Iron_Oxide Sulfate Perchlorates Phosphate Ca_Sulfate Carbonate
+##  0:13        0:9        0: 4    0:15         0:11      0:10       0: 1     
+##  1: 3        1:7        1:12    1: 1         1: 5      1: 6       1:15     
+##                                                                            
+##                                                                            
+##                                                                            
+##                                                                            
+##                                                                            
+##  Fe_Mg_clay Fe_Mg_carbonate Mg_sulfate Phyllosilicates Chlorite Halite
+##  0:13       0:14            0:13       0:12            0:14     0:13  
+##  1: 3       1: 2            1: 3       1: 4            1: 2     1: 3  
+##                                                                       
+##                                                                       
+##                                                                       
+##                                                                       
+##                                                                       
+##  Organic_matter Hydrated_Ca_Sulfate Hydrated_Sulfates Hydrated_Mg_Fe_Sulfate
+##  0: 5           0:14                0:14              0:13                  
+##  1:11           1: 2                1: 2              1: 3                  
+##                                                                             
+##                                                                             
+##                                                                             
+##                                                                             
+##                                                                             
+##  Na_Perchlorate Amorphous_Silicate Hydrated_Carbonates Disordered_Silicates
+##  0:15           0:9                0:16                0:14                
+##  1: 1           1:7                                    1: 2                
+##                                                                            
+##                                                                            
+##                                                                            
+##                                                                            
+##                                                                            
+##  Hydrated_Iron_Oxide Sulfate+Organic_Matter Other_hydrated_phases Kaolinite
+##  0:15                0:11                   0:8                   0:13     
+##  1: 1                1: 5                   1:8                   1: 3     
+##                                                                            
+##                                                                            
+##                                                                            
+##                                                                            
+##                                                                            
+##  Chromite Ilmenite Zircon/Baddeleyite Spinels
+##  0:14     0:14     0:14               0:14   
+##  1: 2     1: 2     1: 2               1: 2   
+##                                              
+##                                              
+##                                              
+##                                              
+## 
+
# Create a matrix containing only the numeric measurements.  The remaining features are metadata about the sample. 
+lithology.matrix <- sapply(lithology.df[,6:40],as.numeric)-1            
+
+# Review the structure of our matrix
+str(lithology.matrix)
+
##  num [1:16, 1:35] 0 0 0 0 0 0 0 1 1 0 ...
+##  - attr(*, "dimnames")=List of 2
+##   ..$ : NULL
+##   ..$ : chr [1:35] "feldspar" "plagioclase" "pyroxene" "olivine" ...
+
+
+

3.2 Data Set B: Load the +PIXL Data

+

The PIXL data provides summaries of the mineral compositions measured +at selected sample sites by the PIXL instrument. Note that here we scale +pixl.mat so features have mean 0 and standard deviation so results will +be different than in Assignment 1.

+
# Load the saved PIXL data with locations added
+pixl.df <- readRDS("/academics/MATP-4910-F24/DAR-Mars-F24/Data/samples_pixl_wide.Rds")
+
+# Convert to factors
+pixl.df[sapply(pixl.df, is.character)] <- lapply(pixl.df[sapply(pixl.df, is.character)], 
+                                       as.factor)
+
+# Review our dataframe
+summary(pixl.df)
+
##      sample           Na20            Mgo             Al203       
+##  Min.   : 1.00   Min.   :1.000   Min.   : 0.730   Min.   : 1.700  
+##  1st Qu.: 4.75   1st Qu.:1.853   1st Qu.: 2.533   1st Qu.: 2.220  
+##  Median : 8.50   Median :1.900   Median :12.800   Median : 3.710  
+##  Mean   : 8.50   Mean   :2.672   Mean   :11.682   Mean   : 5.072  
+##  3rd Qu.:12.25   3rd Qu.:4.500   3rd Qu.:19.100   3rd Qu.: 7.117  
+##  Max.   :16.00   Max.   :5.550   Max.   :22.700   Max.   :11.600  
+##                                                                   
+##       Si02            P205             S03               Cl       
+##  Min.   :22.60   Min.   :0.1000   Min.   : 0.780   Min.   :0.400  
+##  1st Qu.:31.22   1st Qu.:0.2350   1st Qu.: 1.495   1st Qu.:0.940  
+##  Median :38.85   Median :0.5250   Median : 2.600   Median :1.740  
+##  Mean   :38.55   Mean   :0.6512   Mean   : 5.562   Mean   :1.846  
+##  3rd Qu.:41.17   3rd Qu.:0.8400   3rd Qu.: 3.800   3rd Qu.:2.080  
+##  Max.   :57.10   Max.   :2.7600   Max.   :21.530   Max.   :4.500  
+##                                                                   
+##       K20              Cao             Ti02            Cr203      
+##  Min.   :0.0000   Min.   :1.500   Min.   :0.2000   Min.   :0.000  
+##  1st Qu.:0.1600   1st Qu.:2.655   1st Qu.:0.5900   1st Qu.:0.025  
+##  Median :0.2000   Median :3.120   Median :0.7000   Median :0.155  
+##  Mean   :0.5800   Mean   :3.688   Mean   :0.8194   Mean   :0.355  
+##  3rd Qu.:0.8275   3rd Qu.:4.310   3rd Qu.:0.9900   3rd Qu.:0.290  
+##  Max.   :1.9000   Max.   :7.770   Max.   :2.4900   Max.   :1.900  
+##                                                                   
+##       Mno             FeO-T               name             type  
+##  Min.   :0.1000   Min.   :13.24   Atsah     : 1   Igneous    :8  
+##  1st Qu.:0.2800   1st Qu.:16.71   Bearwallow: 1   N/A        :1  
+##  Median :0.4000   Median :23.86   Coulettes : 1   Sedimentary:7  
+##  Mean   :0.3812   Mean   :21.45   Hahonih   : 1                  
+##  3rd Qu.:0.4900   3rd Qu.:25.70   Hazeltop  : 1                  
+##  Max.   :0.6900   Max.   :30.05   Kukaklek  : 1                  
+##                                   (Other)   :10                  
+##          campaign    location          abrasion
+##  Crater Floor:9   01     : 1   Alfalfa     :2  
+##  Delta Front :7   02     : 1   Bellegrade  :2  
+##                   03     : 1   Berry Hollow:2  
+##                   04     : 1   Dourbes     :2  
+##                   05     : 1   Novarupta   :2  
+##                   06     : 1   Quartier    :2  
+##                   (Other):10   (Other)     :4
+
# Make the matrix of just mineral percentage measurements
+pixl.matrix <- pixl.df[,2:14] %>% scale()
+
+# Review the structure
+str(pixl.matrix)
+
##  num [1:16, 1:13] 1.928 1.338 -0.498 -0.538 1.225 ...
+##  - attr(*, "dimnames")=List of 2
+##   ..$ : NULL
+##   ..$ : chr [1:13] "Na20" "Mgo" "Al203" "Si02" ...
+##  - attr(*, "scaled:center")= Named num [1:13] 2.672 11.682 5.072 38.554 0.651 ...
+##   ..- attr(*, "names")= chr [1:13] "Na20" "Mgo" "Al203" "Si02" ...
+##  - attr(*, "scaled:scale")= Named num [1:13] 1.492 7.957 3.75 11.026 0.694 ...
+##   ..- attr(*, "names")= chr [1:13] "Na20" "Mgo" "Al203" "Si02" ...
+
+
+

3.3 Data Set C: Load the +LIBS Data

+

The LIBS data provides summaries of the mineral compositions measured +at selected sample sites by the LIBS instrument, part of the +Perseverance SuperCam.

+
# Load the saved LIBS data with locations added
+libs.df <- readRDS("/academics/MATP-4910-F24/DAR-Mars-F24/Data/supercam_libs_moc_loc.Rds")
+
+#Drop  features that are not to be used in the analysis for this notebook
+libs.df <- libs.df %>% 
+  select(!(c(distance_mm,Tot.Em.,SiO2_stdev,TiO2_stdev,Al2O3_stdev,FeOT_stdev,
+             MgO_stdev,Na2O_stdev,CaO_stdev,K2O_stdev,Total)))
+
+# Convert the points to numeric
+libs.df$point <- as.numeric(libs.df$point)
+
+# Review what we have
+summary(libs.df)
+
##       sol              lat             lon           target         
+##  Min.   :  15.0   Min.   :18.43   Min.   :77.34   Length:1932       
+##  1st Qu.: 281.0   1st Qu.:18.44   1st Qu.:77.36   Class :character  
+##  Median : 557.0   Median :18.46   Median :77.40   Mode  :character  
+##  Mean   : 565.1   Mean   :18.46   Mean   :77.40                     
+##  3rd Qu.: 872.0   3rd Qu.:18.48   3rd Qu.:77.44                     
+##  Max.   :1019.0   Max.   :18.50   Max.   :77.45                     
+##      point             SiO2            TiO2            Al2O3       
+##  Min.   : 1.000   Min.   : 0.00   Min.   :0.0000   Min.   : 0.000  
+##  1st Qu.: 3.000   1st Qu.:42.04   1st Qu.:0.0300   1st Qu.: 3.080  
+##  Median : 5.000   Median :45.80   Median :0.3200   Median : 4.925  
+##  Mean   : 5.776   Mean   :43.47   Mean   :0.3719   Mean   : 6.246  
+##  3rd Qu.: 8.000   3rd Qu.:49.23   3rd Qu.:0.6400   3rd Qu.: 8.533  
+##  Max.   :28.000   Max.   :76.12   Max.   :2.4000   Max.   :38.350  
+##       FeOT            MgO             CaO              Na2O       
+##  Min.   : 0.29   Min.   : 0.29   Min.   : 0.080   Min.   :0.0000  
+##  1st Qu.:13.27   1st Qu.: 5.72   1st Qu.: 1.830   1st Qu.:0.9775  
+##  Median :20.21   Median :12.78   Median : 3.625   Median :1.5200  
+##  Mean   :20.07   Mean   :16.47   Mean   : 4.726   Mean   :1.7600  
+##  3rd Qu.:25.45   3rd Qu.:27.83   3rd Qu.: 4.622   3rd Qu.:2.4000  
+##  Max.   :82.68   Max.   :45.21   Max.   :52.130   Max.   :7.5200  
+##       K2O         
+##  Min.   : 0.0000  
+##  1st Qu.: 0.0000  
+##  Median : 0.3000  
+##  Mean   : 0.5909  
+##  3rd Qu.: 0.7800  
+##  Max.   :34.8700
+
# Make the a matrix contain only the libs measurements for each mineral
+libs.matrix <- as.matrix(libs.df[,6:13]) 
+
+# Check to see scaling
+str(libs.matrix)
+
##  num [1:1932, 1:8] 49.7 55.8 61.2 51 48 ...
+##  - attr(*, "dimnames")=List of 2
+##   ..$ : NULL
+##   ..$ : chr [1:8] "SiO2" "TiO2" "Al2O3" "FeOT" ...
+
+
+

3.4 Dataset D: Load the +SHERLOC Data

+

The SHERLOC data you will be using for this lab is the result of +scientists’ interpretations of extensive spectral analysis of abrasion +samples provided by the SHERLOC instrument.

+

NOTE: This dataset presents minerals as rows and +sample sites as columns. You’ll probably want to rotate the dataset for +easier analysis….

+
# Read in data as provided.  
+sherloc_abrasion_raw <- readRDS("/academics/MATP-4910-F24/DAR-Mars-F24/Data/abrasions_sherloc_samples.Rds")
+
+# Clean up data types
+sherloc_abrasion_raw$Mineral<-as.factor(sherloc_abrasion_raw$Mineral)
+sherloc_abrasion_raw[sapply(sherloc_abrasion_raw, is.character)] <- lapply(sherloc_abrasion_raw[sapply(sherloc_abrasion_raw, is.character)], 
+                                       as.numeric)
+# Transform NA's to 0
+sherloc_abrasion_raw <- sherloc_abrasion_raw %>% replace(is.na(.), 0)
+
+# Reformat data so that rows are "abrasions" and columns list the presence of minerals. 
+# Do this by "pivoting" to a long format, and then back to the desired wide format.  
+
+sherloc_long <- sherloc_abrasion_raw %>%
+  pivot_longer(!Mineral, names_to = "Name", values_to = "Presence")
+
+# Make abrasion a factor 
+sherloc_long$Name <- as.factor(sherloc_long$Name)
+
+# Make it a matrix
+sherloc.matrix <- sherloc_long %>%
+  pivot_wider(names_from = Mineral, values_from = Presence)
+
+# Get sample information from PIXL and add to measurements -- assumes order is the same
+
+sherloc.df <- cbind(pixl.df[,c("sample","type","campaign","abrasion")],sherloc.matrix)
+
+# Review what we have
+summary(sherloc.df)
+
##      sample               type           campaign         abrasion
+##  Min.   : 1.00   Igneous    :8   Crater Floor:9   Alfalfa     :2  
+##  1st Qu.: 4.75   N/A        :1   Delta Front :7   Bellegrade  :2  
+##  Median : 8.50   Sedimentary:7                    Berry Hollow:2  
+##  Mean   : 8.50                                    Dourbes     :2  
+##  3rd Qu.:12.25                                    Novarupta   :2  
+##  Max.   :16.00                                    Quartier    :2  
+##                                                   (Other)     :4  
+##          Name     Plagioclase        Sulfate         Ca-sulfate    
+##  Atsah     : 1   Min.   :0.0000   Min.   :0.0000   Min.   :0.0000  
+##  Bearwallow: 1   1st Qu.:0.0000   1st Qu.:0.1875   1st Qu.:0.0000  
+##  Coulettes : 1   Median :0.0000   Median :1.0000   Median :0.0000  
+##  Hahonih   : 1   Mean   :0.1875   Mean   :0.6562   Mean   :0.3438  
+##  Hazeltop  : 1   3rd Qu.:0.0000   3rd Qu.:1.0000   3rd Qu.:1.0000  
+##  Kukaklek  : 1   Max.   :1.0000   Max.   :1.0000   Max.   :1.0000  
+##  (Other)   :10                                                     
+##  Hydrated Ca-sulfate   Mg-sulfate     Hydrated Sulfates Hydrated Mg-Fe sulfate
+##  Min.   :0.000       Min.   :0.0000   Min.   :0.000     Min.   :0.0000        
+##  1st Qu.:0.000       1st Qu.:0.0000   1st Qu.:0.000     1st Qu.:0.0000        
+##  Median :0.000       Median :0.0000   Median :0.000     Median :0.0000        
+##  Mean   :0.125       Mean   :0.1875   Mean   :0.125     Mean   :0.1875        
+##  3rd Qu.:0.000       3rd Qu.:0.0000   3rd Qu.:0.000     3rd Qu.:0.0000        
+##  Max.   :1.000       Max.   :1.0000   Max.   :1.000     Max.   :1.0000        
+##                                                                               
+##   Perchlorates    Na-perchlorate    Amorphous Silicate   Phosphate     
+##  Min.   :0.0000   Min.   :0.00000   Min.   :0.0000     Min.   :0.0000  
+##  1st Qu.:0.0000   1st Qu.:0.00000   1st Qu.:0.0000     1st Qu.:0.0000  
+##  Median :0.0000   Median :0.00000   Median :0.0000     Median :0.0000  
+##  Mean   :0.0625   Mean   :0.03125   Mean   :0.1406     Mean   :0.2031  
+##  3rd Qu.:0.0000   3rd Qu.:0.00000   3rd Qu.:0.2500     3rd Qu.:0.3125  
+##  Max.   :1.0000   Max.   :0.50000   Max.   :0.5000     Max.   :1.0000  
+##                                                                        
+##     Pyroxene         Olivine         Carbonate      Fe-Mg carbonate
+##  Min.   :0.0000   Min.   :0.0000   Min.   :0.0000   Min.   :0.000  
+##  1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.4375   1st Qu.:0.000  
+##  Median :1.0000   Median :0.6250   Median :1.0000   Median :0.000  
+##  Mean   :0.6875   Mean   :0.5312   Mean   :0.7344   Mean   :0.125  
+##  3rd Qu.:1.0000   3rd Qu.:1.0000   3rd Qu.:1.0000   3rd Qu.:0.000  
+##  Max.   :1.0000   Max.   :1.0000   Max.   :1.0000   Max.   :1.000  
+##                                                                    
+##  Hydrated Carbonates Disordered Silicates    Feldspar         Quartz       
+##  Min.   :0           Min.   :0.000        Min.   :0.000   Min.   :0.00000  
+##  1st Qu.:0           1st Qu.:0.000        1st Qu.:0.000   1st Qu.:0.00000  
+##  Median :0           Median :0.000        Median :0.000   Median :0.00000  
+##  Mean   :0           Mean   :0.125        Mean   :0.125   Mean   :0.03125  
+##  3rd Qu.:0           3rd Qu.:0.000        3rd Qu.:0.000   3rd Qu.:0.00000  
+##  Max.   :0           Max.   :1.000        Max.   :1.000   Max.   :0.25000  
+##                                                                            
+##     Apatite        FeTi oxides         Halite          Iron oxide    
+##  Min.   :0.0000   Min.   :0.0000   Min.   :0.00000   Min.   :0.0000  
+##  1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.00000   1st Qu.:0.0000  
+##  Median :0.0000   Median :0.0000   Median :0.00000   Median :0.0000  
+##  Mean   :0.1406   Mean   :0.1406   Mean   :0.04688   Mean   :0.2812  
+##  3rd Qu.:0.0000   3rd Qu.:0.0000   3rd Qu.:0.00000   3rd Qu.:0.5000  
+##  Max.   :1.0000   Max.   :1.0000   Max.   :0.25000   Max.   :1.0000  
+##                                                                      
+##  Hydrated Iron oxide Organic matter   Sulfate+Organic matter
+##  Min.   :0.00000     Min.   :0.0000   Min.   :0.0000        
+##  1st Qu.:0.00000     1st Qu.:0.0000   1st Qu.:0.0000        
+##  Median :0.00000     Median :1.0000   Median :0.0000        
+##  Mean   :0.01562     Mean   :0.5938   Mean   :0.2188        
+##  3rd Qu.:0.00000     3rd Qu.:1.0000   3rd Qu.:0.2500        
+##  Max.   :0.25000     Max.   :1.0000   Max.   :1.0000        
+##                                                             
+##  Other hydrated phases Phyllosilicates      Chlorite     
+##  Min.   :0.0000        Min.   :0.00000   Min.   :0.0000  
+##  1st Qu.:0.0000        1st Qu.:0.00000   1st Qu.:0.0000  
+##  Median :0.2500        Median :0.00000   Median :0.0000  
+##  Mean   :0.4375        Mean   :0.09375   Mean   :0.0625  
+##  3rd Qu.:1.0000        3rd Qu.:0.06250   3rd Qu.:0.0000  
+##  Max.   :1.0000        Max.   :0.50000   Max.   :0.5000  
+##                                                          
+##  Kaolinite (hydrous Al-clay)    Chromite        Ilmenite     Zircon/Baddeleyite
+##  Min.   :0.0000              Min.   :0.000   Min.   :0.000   Min.   :0.000     
+##  1st Qu.:0.0000              1st Qu.:0.000   1st Qu.:0.000   1st Qu.:0.000     
+##  Median :0.0000              Median :0.000   Median :0.000   Median :0.000     
+##  Mean   :0.1875              Mean   :0.125   Mean   :0.125   Mean   :0.125     
+##  3rd Qu.:0.0000              3rd Qu.:0.000   3rd Qu.:0.000   3rd Qu.:0.000     
+##  Max.   :1.0000              Max.   :1.000   Max.   :1.000   Max.   :1.000     
+##                                                                                
+##  Fe-Mg-clay minerals    Spinels      
+##  Min.   :0.0000      Min.   :0.0000  
+##  1st Qu.:0.0000      1st Qu.:0.0000  
+##  Median :0.0000      Median :0.0000  
+##  Mean   :0.1875      Mean   :0.0625  
+##  3rd Qu.:0.0000      3rd Qu.:0.0000  
+##  Max.   :1.0000      Max.   :0.5000  
+## 
+
# Measurements are everything except first column
+sherloc.matrix<-as.matrix(sherloc.matrix[,-1])
+
+# Sherlock measurement matrix
+# Review the structure 
+str(sherloc.matrix)
+
##  num [1:16, 1:35] 1 1 1 0 0 0 0 0 0 0 ...
+##  - attr(*, "dimnames")=List of 2
+##   ..$ : NULL
+##   ..$ : chr [1:35] "Plagioclase" "Sulfate" "Ca-sulfate" "Hydrated Ca-sulfate" ...
+
+
+

3.5 Data Set E: PIXL + +Sherloc

+
# Combine PIXL and SHERLOC dataframes 
+pixl_sherloc.df <- cbind(pixl.df,sherloc.df )
+
+# Review what we have
+summary(pixl_sherloc.df)
+
##      sample           Na20            Mgo             Al203       
+##  Min.   : 1.00   Min.   :1.000   Min.   : 0.730   Min.   : 1.700  
+##  1st Qu.: 4.75   1st Qu.:1.853   1st Qu.: 2.533   1st Qu.: 2.220  
+##  Median : 8.50   Median :1.900   Median :12.800   Median : 3.710  
+##  Mean   : 8.50   Mean   :2.672   Mean   :11.682   Mean   : 5.072  
+##  3rd Qu.:12.25   3rd Qu.:4.500   3rd Qu.:19.100   3rd Qu.: 7.117  
+##  Max.   :16.00   Max.   :5.550   Max.   :22.700   Max.   :11.600  
+##                                                                   
+##       Si02            P205             S03               Cl       
+##  Min.   :22.60   Min.   :0.1000   Min.   : 0.780   Min.   :0.400  
+##  1st Qu.:31.22   1st Qu.:0.2350   1st Qu.: 1.495   1st Qu.:0.940  
+##  Median :38.85   Median :0.5250   Median : 2.600   Median :1.740  
+##  Mean   :38.55   Mean   :0.6512   Mean   : 5.562   Mean   :1.846  
+##  3rd Qu.:41.17   3rd Qu.:0.8400   3rd Qu.: 3.800   3rd Qu.:2.080  
+##  Max.   :57.10   Max.   :2.7600   Max.   :21.530   Max.   :4.500  
+##                                                                   
+##       K20              Cao             Ti02            Cr203      
+##  Min.   :0.0000   Min.   :1.500   Min.   :0.2000   Min.   :0.000  
+##  1st Qu.:0.1600   1st Qu.:2.655   1st Qu.:0.5900   1st Qu.:0.025  
+##  Median :0.2000   Median :3.120   Median :0.7000   Median :0.155  
+##  Mean   :0.5800   Mean   :3.688   Mean   :0.8194   Mean   :0.355  
+##  3rd Qu.:0.8275   3rd Qu.:4.310   3rd Qu.:0.9900   3rd Qu.:0.290  
+##  Max.   :1.9000   Max.   :7.770   Max.   :2.4900   Max.   :1.900  
+##                                                                   
+##       Mno             FeO-T               name             type  
+##  Min.   :0.1000   Min.   :13.24   Atsah     : 1   Igneous    :8  
+##  1st Qu.:0.2800   1st Qu.:16.71   Bearwallow: 1   N/A        :1  
+##  Median :0.4000   Median :23.86   Coulettes : 1   Sedimentary:7  
+##  Mean   :0.3812   Mean   :21.45   Hahonih   : 1                  
+##  3rd Qu.:0.4900   3rd Qu.:25.70   Hazeltop  : 1                  
+##  Max.   :0.6900   Max.   :30.05   Kukaklek  : 1                  
+##                                   (Other)   :10                  
+##          campaign    location          abrasion     sample               type  
+##  Crater Floor:9   01     : 1   Alfalfa     :2   Min.   : 1.00   Igneous    :8  
+##  Delta Front :7   02     : 1   Bellegrade  :2   1st Qu.: 4.75   N/A        :1  
+##                   03     : 1   Berry Hollow:2   Median : 8.50   Sedimentary:7  
+##                   04     : 1   Dourbes     :2   Mean   : 8.50                  
+##                   05     : 1   Novarupta   :2   3rd Qu.:12.25                  
+##                   06     : 1   Quartier    :2   Max.   :16.00                  
+##                   (Other):10   (Other)     :4                                  
+##          campaign         abrasion         Name     Plagioclase    
+##  Crater Floor:9   Alfalfa     :2   Atsah     : 1   Min.   :0.0000  
+##  Delta Front :7   Bellegrade  :2   Bearwallow: 1   1st Qu.:0.0000  
+##                   Berry Hollow:2   Coulettes : 1   Median :0.0000  
+##                   Dourbes     :2   Hahonih   : 1   Mean   :0.1875  
+##                   Novarupta   :2   Hazeltop  : 1   3rd Qu.:0.0000  
+##                   Quartier    :2   Kukaklek  : 1   Max.   :1.0000  
+##                   (Other)     :4   (Other)   :10                   
+##     Sulfate         Ca-sulfate     Hydrated Ca-sulfate   Mg-sulfate    
+##  Min.   :0.0000   Min.   :0.0000   Min.   :0.000       Min.   :0.0000  
+##  1st Qu.:0.1875   1st Qu.:0.0000   1st Qu.:0.000       1st Qu.:0.0000  
+##  Median :1.0000   Median :0.0000   Median :0.000       Median :0.0000  
+##  Mean   :0.6562   Mean   :0.3438   Mean   :0.125       Mean   :0.1875  
+##  3rd Qu.:1.0000   3rd Qu.:1.0000   3rd Qu.:0.000       3rd Qu.:0.0000  
+##  Max.   :1.0000   Max.   :1.0000   Max.   :1.000       Max.   :1.0000  
+##                                                                        
+##  Hydrated Sulfates Hydrated Mg-Fe sulfate  Perchlorates    Na-perchlorate   
+##  Min.   :0.000     Min.   :0.0000         Min.   :0.0000   Min.   :0.00000  
+##  1st Qu.:0.000     1st Qu.:0.0000         1st Qu.:0.0000   1st Qu.:0.00000  
+##  Median :0.000     Median :0.0000         Median :0.0000   Median :0.00000  
+##  Mean   :0.125     Mean   :0.1875         Mean   :0.0625   Mean   :0.03125  
+##  3rd Qu.:0.000     3rd Qu.:0.0000         3rd Qu.:0.0000   3rd Qu.:0.00000  
+##  Max.   :1.000     Max.   :1.0000         Max.   :1.0000   Max.   :0.50000  
+##                                                                             
+##  Amorphous Silicate   Phosphate         Pyroxene         Olivine      
+##  Min.   :0.0000     Min.   :0.0000   Min.   :0.0000   Min.   :0.0000  
+##  1st Qu.:0.0000     1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.0000  
+##  Median :0.0000     Median :0.0000   Median :1.0000   Median :0.6250  
+##  Mean   :0.1406     Mean   :0.2031   Mean   :0.6875   Mean   :0.5312  
+##  3rd Qu.:0.2500     3rd Qu.:0.3125   3rd Qu.:1.0000   3rd Qu.:1.0000  
+##  Max.   :0.5000     Max.   :1.0000   Max.   :1.0000   Max.   :1.0000  
+##                                                                       
+##    Carbonate      Fe-Mg carbonate Hydrated Carbonates Disordered Silicates
+##  Min.   :0.0000   Min.   :0.000   Min.   :0           Min.   :0.000       
+##  1st Qu.:0.4375   1st Qu.:0.000   1st Qu.:0           1st Qu.:0.000       
+##  Median :1.0000   Median :0.000   Median :0           Median :0.000       
+##  Mean   :0.7344   Mean   :0.125   Mean   :0           Mean   :0.125       
+##  3rd Qu.:1.0000   3rd Qu.:0.000   3rd Qu.:0           3rd Qu.:0.000       
+##  Max.   :1.0000   Max.   :1.000   Max.   :0           Max.   :1.000       
+##                                                                           
+##     Feldspar         Quartz           Apatite        FeTi oxides    
+##  Min.   :0.000   Min.   :0.00000   Min.   :0.0000   Min.   :0.0000  
+##  1st Qu.:0.000   1st Qu.:0.00000   1st Qu.:0.0000   1st Qu.:0.0000  
+##  Median :0.000   Median :0.00000   Median :0.0000   Median :0.0000  
+##  Mean   :0.125   Mean   :0.03125   Mean   :0.1406   Mean   :0.1406  
+##  3rd Qu.:0.000   3rd Qu.:0.00000   3rd Qu.:0.0000   3rd Qu.:0.0000  
+##  Max.   :1.000   Max.   :0.25000   Max.   :1.0000   Max.   :1.0000  
+##                                                                     
+##      Halite          Iron oxide     Hydrated Iron oxide Organic matter  
+##  Min.   :0.00000   Min.   :0.0000   Min.   :0.00000     Min.   :0.0000  
+##  1st Qu.:0.00000   1st Qu.:0.0000   1st Qu.:0.00000     1st Qu.:0.0000  
+##  Median :0.00000   Median :0.0000   Median :0.00000     Median :1.0000  
+##  Mean   :0.04688   Mean   :0.2812   Mean   :0.01562     Mean   :0.5938  
+##  3rd Qu.:0.00000   3rd Qu.:0.5000   3rd Qu.:0.00000     3rd Qu.:1.0000  
+##  Max.   :0.25000   Max.   :1.0000   Max.   :0.25000     Max.   :1.0000  
+##                                                                         
+##  Sulfate+Organic matter Other hydrated phases Phyllosilicates  
+##  Min.   :0.0000         Min.   :0.0000        Min.   :0.00000  
+##  1st Qu.:0.0000         1st Qu.:0.0000        1st Qu.:0.00000  
+##  Median :0.0000         Median :0.2500        Median :0.00000  
+##  Mean   :0.2188         Mean   :0.4375        Mean   :0.09375  
+##  3rd Qu.:0.2500         3rd Qu.:1.0000        3rd Qu.:0.06250  
+##  Max.   :1.0000         Max.   :1.0000        Max.   :0.50000  
+##                                                                
+##     Chlorite      Kaolinite (hydrous Al-clay)    Chromite        Ilmenite    
+##  Min.   :0.0000   Min.   :0.0000              Min.   :0.000   Min.   :0.000  
+##  1st Qu.:0.0000   1st Qu.:0.0000              1st Qu.:0.000   1st Qu.:0.000  
+##  Median :0.0000   Median :0.0000              Median :0.000   Median :0.000  
+##  Mean   :0.0625   Mean   :0.1875              Mean   :0.125   Mean   :0.125  
+##  3rd Qu.:0.0000   3rd Qu.:0.0000              3rd Qu.:0.000   3rd Qu.:0.000  
+##  Max.   :0.5000   Max.   :1.0000              Max.   :1.000   Max.   :1.000  
+##                                                                              
+##  Zircon/Baddeleyite Fe-Mg-clay minerals    Spinels      
+##  Min.   :0.000      Min.   :0.0000      Min.   :0.0000  
+##  1st Qu.:0.000      1st Qu.:0.0000      1st Qu.:0.0000  
+##  Median :0.000      Median :0.0000      Median :0.0000  
+##  Mean   :0.125      Mean   :0.1875      Mean   :0.0625  
+##  3rd Qu.:0.000      3rd Qu.:0.0000      3rd Qu.:0.0000  
+##  Max.   :1.000      Max.   :1.0000      Max.   :0.5000  
+## 
+
# Combine PIXL and SHERLOC matrices
+pixl_sherloc.matrix<-cbind(pixl.matrix,sherloc.matrix)
+
+# Review the structure of our matrix
+str(pixl_sherloc.matrix)
+
##  num [1:16, 1:48] 1.928 1.338 -0.498 -0.538 1.225 ...
+##  - attr(*, "dimnames")=List of 2
+##   ..$ : NULL
+##   ..$ : chr [1:48] "Na20" "Mgo" "Al203" "Si02" ...
+
+
+

3.6 Data Set F: PIXL + +Lithography

+

Create data and matrix from prior datasets

+
# Combine our PIXL and Lithology dataframes
+pixl_lithology.df <- cbind(pixl.df,lithology.df )
+
+# Review what we have
+summary(pixl_lithology.df)
+
##      sample           Na20            Mgo             Al203       
+##  Min.   : 1.00   Min.   :1.000   Min.   : 0.730   Min.   : 1.700  
+##  1st Qu.: 4.75   1st Qu.:1.853   1st Qu.: 2.533   1st Qu.: 2.220  
+##  Median : 8.50   Median :1.900   Median :12.800   Median : 3.710  
+##  Mean   : 8.50   Mean   :2.672   Mean   :11.682   Mean   : 5.072  
+##  3rd Qu.:12.25   3rd Qu.:4.500   3rd Qu.:19.100   3rd Qu.: 7.117  
+##  Max.   :16.00   Max.   :5.550   Max.   :22.700   Max.   :11.600  
+##                                                                   
+##       Si02            P205             S03               Cl       
+##  Min.   :22.60   Min.   :0.1000   Min.   : 0.780   Min.   :0.400  
+##  1st Qu.:31.22   1st Qu.:0.2350   1st Qu.: 1.495   1st Qu.:0.940  
+##  Median :38.85   Median :0.5250   Median : 2.600   Median :1.740  
+##  Mean   :38.55   Mean   :0.6512   Mean   : 5.562   Mean   :1.846  
+##  3rd Qu.:41.17   3rd Qu.:0.8400   3rd Qu.: 3.800   3rd Qu.:2.080  
+##  Max.   :57.10   Max.   :2.7600   Max.   :21.530   Max.   :4.500  
+##                                                                   
+##       K20              Cao             Ti02            Cr203      
+##  Min.   :0.0000   Min.   :1.500   Min.   :0.2000   Min.   :0.000  
+##  1st Qu.:0.1600   1st Qu.:2.655   1st Qu.:0.5900   1st Qu.:0.025  
+##  Median :0.2000   Median :3.120   Median :0.7000   Median :0.155  
+##  Mean   :0.5800   Mean   :3.688   Mean   :0.8194   Mean   :0.355  
+##  3rd Qu.:0.8275   3rd Qu.:4.310   3rd Qu.:0.9900   3rd Qu.:0.290  
+##  Max.   :1.9000   Max.   :7.770   Max.   :2.4900   Max.   :1.900  
+##                                                                   
+##       Mno             FeO-T               name             type  
+##  Min.   :0.1000   Min.   :13.24   Atsah     : 1   Igneous    :8  
+##  1st Qu.:0.2800   1st Qu.:16.71   Bearwallow: 1   N/A        :1  
+##  Median :0.4000   Median :23.86   Coulettes : 1   Sedimentary:7  
+##  Mean   :0.3812   Mean   :21.45   Hahonih   : 1                  
+##  3rd Qu.:0.4900   3rd Qu.:25.70   Hazeltop  : 1                  
+##  Max.   :0.6900   Max.   :30.05   Kukaklek  : 1                  
+##                                   (Other)   :10                  
+##          campaign    location          abrasion     sample              name   
+##  Crater Floor:9   01     : 1   Alfalfa     :2   Min.   : 1.00   Atsah     : 1  
+##  Delta Front :7   02     : 1   Bellegrade  :2   1st Qu.: 4.75   Bearwallow: 1  
+##                   03     : 1   Berry Hollow:2   Median : 8.50   Coulettes : 1  
+##                   04     : 1   Dourbes     :2   Mean   : 8.50   Hahonih   : 1  
+##                   05     : 1   Novarupta   :2   3rd Qu.:12.25   Hazeltop  : 1  
+##                   06     : 1   Quartier    :2   Max.   :16.00   Kukaklek  : 1  
+##                   (Other):10   (Other)     :4                   (Other)   :10  
+##        SampleType         campaign         abrasion feldspar plagioclase
+##  atmospheric: 1   Crater Floor:9   Alfalfa     :2   0:14     0:13       
+##  regolith   : 0   Delta Front :7   Bellegarde  :2   1: 2     1: 3       
+##  rock core  :15   Margin Unit :0   Berry Hollow:2                       
+##                                    Dourbes     :2                       
+##                                    Novarupta   :2                       
+##                                    Quartier    :2                       
+##                                    (Other)     :4                       
+##  pyroxene olivine quartz apatite FeTi_Oxides Iron_Oxide Sulfate Perchlorates
+##  0: 5     0: 6    0:14   0:13    0:13        0:9        0: 4    0:15        
+##  1:11     1:10    1: 2   1: 3    1: 3        1:7        1:12    1: 1        
+##                                                                             
+##                                                                             
+##                                                                             
+##                                                                             
+##                                                                             
+##  Phosphate Ca_Sulfate Carbonate Fe_Mg_clay Fe_Mg_carbonate Mg_sulfate
+##  0:11      0:10       0: 1      0:13       0:14            0:13      
+##  1: 5      1: 6       1:15      1: 3       1: 2            1: 3      
+##                                                                      
+##                                                                      
+##                                                                      
+##                                                                      
+##                                                                      
+##  Phyllosilicates Chlorite Halite Organic_matter Hydrated_Ca_Sulfate
+##  0:12            0:14     0:13   0: 5           0:14               
+##  1: 4            1: 2     1: 3   1:11           1: 2               
+##                                                                    
+##                                                                    
+##                                                                    
+##                                                                    
+##                                                                    
+##  Hydrated_Sulfates Hydrated_Mg_Fe_Sulfate Na_Perchlorate Amorphous_Silicate
+##  0:14              0:13                   0:15           0:9               
+##  1: 2              1: 3                   1: 1           1:7               
+##                                                                            
+##                                                                            
+##                                                                            
+##                                                                            
+##                                                                            
+##  Hydrated_Carbonates Disordered_Silicates Hydrated_Iron_Oxide
+##  0:16                0:14                 0:15               
+##                      1: 2                 1: 1               
+##                                                              
+##                                                              
+##                                                              
+##                                                              
+##                                                              
+##  Sulfate+Organic_Matter Other_hydrated_phases Kaolinite Chromite Ilmenite
+##  0:11                   0:8                   0:13      0:14     0:14    
+##  1: 5                   1:8                   1: 3      1: 2     1: 2    
+##                                                                          
+##                                                                          
+##                                                                          
+##                                                                          
+##                                                                          
+##  Zircon/Baddeleyite Spinels
+##  0:14               0:14   
+##  1: 2               1: 2   
+##                            
+##                            
+##                            
+##                            
+## 
+
# Combine PIXL and Lithology matrices
+pixl_lithology.matrix<-cbind(pixl.matrix,lithology.matrix)
+
+# Review the structure
+str(pixl_lithology.matrix)
+
##  num [1:16, 1:48] 1.928 1.338 -0.498 -0.538 1.225 ...
+##  - attr(*, "dimnames")=List of 2
+##   ..$ : NULL
+##   ..$ : chr [1:48] "Na20" "Mgo" "Al203" "Si02" ...
+
+
+

3.7 Data Set G: Sherloc + +Lithology

+

Create Data and matrix from prior datasets by taking on appropriate +combinations.

+
# Combine the Lithology and SHERLOC dataframes
+sherloc_lithology.df <- cbind(sherloc.df,lithology.df )
+
+# Review what we have
+summary(sherloc_lithology.df)
+
##      sample               type           campaign         abrasion
+##  Min.   : 1.00   Igneous    :8   Crater Floor:9   Alfalfa     :2  
+##  1st Qu.: 4.75   N/A        :1   Delta Front :7   Bellegrade  :2  
+##  Median : 8.50   Sedimentary:7                    Berry Hollow:2  
+##  Mean   : 8.50                                    Dourbes     :2  
+##  3rd Qu.:12.25                                    Novarupta   :2  
+##  Max.   :16.00                                    Quartier    :2  
+##                                                   (Other)     :4  
+##          Name     Plagioclase        Sulfate         Ca-sulfate    
+##  Atsah     : 1   Min.   :0.0000   Min.   :0.0000   Min.   :0.0000  
+##  Bearwallow: 1   1st Qu.:0.0000   1st Qu.:0.1875   1st Qu.:0.0000  
+##  Coulettes : 1   Median :0.0000   Median :1.0000   Median :0.0000  
+##  Hahonih   : 1   Mean   :0.1875   Mean   :0.6562   Mean   :0.3438  
+##  Hazeltop  : 1   3rd Qu.:0.0000   3rd Qu.:1.0000   3rd Qu.:1.0000  
+##  Kukaklek  : 1   Max.   :1.0000   Max.   :1.0000   Max.   :1.0000  
+##  (Other)   :10                                                     
+##  Hydrated Ca-sulfate   Mg-sulfate     Hydrated Sulfates Hydrated Mg-Fe sulfate
+##  Min.   :0.000       Min.   :0.0000   Min.   :0.000     Min.   :0.0000        
+##  1st Qu.:0.000       1st Qu.:0.0000   1st Qu.:0.000     1st Qu.:0.0000        
+##  Median :0.000       Median :0.0000   Median :0.000     Median :0.0000        
+##  Mean   :0.125       Mean   :0.1875   Mean   :0.125     Mean   :0.1875        
+##  3rd Qu.:0.000       3rd Qu.:0.0000   3rd Qu.:0.000     3rd Qu.:0.0000        
+##  Max.   :1.000       Max.   :1.0000   Max.   :1.000     Max.   :1.0000        
+##                                                                               
+##   Perchlorates    Na-perchlorate    Amorphous Silicate   Phosphate     
+##  Min.   :0.0000   Min.   :0.00000   Min.   :0.0000     Min.   :0.0000  
+##  1st Qu.:0.0000   1st Qu.:0.00000   1st Qu.:0.0000     1st Qu.:0.0000  
+##  Median :0.0000   Median :0.00000   Median :0.0000     Median :0.0000  
+##  Mean   :0.0625   Mean   :0.03125   Mean   :0.1406     Mean   :0.2031  
+##  3rd Qu.:0.0000   3rd Qu.:0.00000   3rd Qu.:0.2500     3rd Qu.:0.3125  
+##  Max.   :1.0000   Max.   :0.50000   Max.   :0.5000     Max.   :1.0000  
+##                                                                        
+##     Pyroxene         Olivine         Carbonate      Fe-Mg carbonate
+##  Min.   :0.0000   Min.   :0.0000   Min.   :0.0000   Min.   :0.000  
+##  1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.4375   1st Qu.:0.000  
+##  Median :1.0000   Median :0.6250   Median :1.0000   Median :0.000  
+##  Mean   :0.6875   Mean   :0.5312   Mean   :0.7344   Mean   :0.125  
+##  3rd Qu.:1.0000   3rd Qu.:1.0000   3rd Qu.:1.0000   3rd Qu.:0.000  
+##  Max.   :1.0000   Max.   :1.0000   Max.   :1.0000   Max.   :1.000  
+##                                                                    
+##  Hydrated Carbonates Disordered Silicates    Feldspar         Quartz       
+##  Min.   :0           Min.   :0.000        Min.   :0.000   Min.   :0.00000  
+##  1st Qu.:0           1st Qu.:0.000        1st Qu.:0.000   1st Qu.:0.00000  
+##  Median :0           Median :0.000        Median :0.000   Median :0.00000  
+##  Mean   :0           Mean   :0.125        Mean   :0.125   Mean   :0.03125  
+##  3rd Qu.:0           3rd Qu.:0.000        3rd Qu.:0.000   3rd Qu.:0.00000  
+##  Max.   :0           Max.   :1.000        Max.   :1.000   Max.   :0.25000  
+##                                                                            
+##     Apatite        FeTi oxides         Halite          Iron oxide    
+##  Min.   :0.0000   Min.   :0.0000   Min.   :0.00000   Min.   :0.0000  
+##  1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.00000   1st Qu.:0.0000  
+##  Median :0.0000   Median :0.0000   Median :0.00000   Median :0.0000  
+##  Mean   :0.1406   Mean   :0.1406   Mean   :0.04688   Mean   :0.2812  
+##  3rd Qu.:0.0000   3rd Qu.:0.0000   3rd Qu.:0.00000   3rd Qu.:0.5000  
+##  Max.   :1.0000   Max.   :1.0000   Max.   :0.25000   Max.   :1.0000  
+##                                                                      
+##  Hydrated Iron oxide Organic matter   Sulfate+Organic matter
+##  Min.   :0.00000     Min.   :0.0000   Min.   :0.0000        
+##  1st Qu.:0.00000     1st Qu.:0.0000   1st Qu.:0.0000        
+##  Median :0.00000     Median :1.0000   Median :0.0000        
+##  Mean   :0.01562     Mean   :0.5938   Mean   :0.2188        
+##  3rd Qu.:0.00000     3rd Qu.:1.0000   3rd Qu.:0.2500        
+##  Max.   :0.25000     Max.   :1.0000   Max.   :1.0000        
+##                                                             
+##  Other hydrated phases Phyllosilicates      Chlorite     
+##  Min.   :0.0000        Min.   :0.00000   Min.   :0.0000  
+##  1st Qu.:0.0000        1st Qu.:0.00000   1st Qu.:0.0000  
+##  Median :0.2500        Median :0.00000   Median :0.0000  
+##  Mean   :0.4375        Mean   :0.09375   Mean   :0.0625  
+##  3rd Qu.:1.0000        3rd Qu.:0.06250   3rd Qu.:0.0000  
+##  Max.   :1.0000        Max.   :0.50000   Max.   :0.5000  
+##                                                          
+##  Kaolinite (hydrous Al-clay)    Chromite        Ilmenite     Zircon/Baddeleyite
+##  Min.   :0.0000              Min.   :0.000   Min.   :0.000   Min.   :0.000     
+##  1st Qu.:0.0000              1st Qu.:0.000   1st Qu.:0.000   1st Qu.:0.000     
+##  Median :0.0000              Median :0.000   Median :0.000   Median :0.000     
+##  Mean   :0.1875              Mean   :0.125   Mean   :0.125   Mean   :0.125     
+##  3rd Qu.:0.0000              3rd Qu.:0.000   3rd Qu.:0.000   3rd Qu.:0.000     
+##  Max.   :1.0000              Max.   :1.000   Max.   :1.000   Max.   :1.000     
+##                                                                                
+##  Fe-Mg-clay minerals    Spinels           sample              name   
+##  Min.   :0.0000      Min.   :0.0000   Min.   : 1.00   Atsah     : 1  
+##  1st Qu.:0.0000      1st Qu.:0.0000   1st Qu.: 4.75   Bearwallow: 1  
+##  Median :0.0000      Median :0.0000   Median : 8.50   Coulettes : 1  
+##  Mean   :0.1875      Mean   :0.0625   Mean   : 8.50   Hahonih   : 1  
+##  3rd Qu.:0.0000      3rd Qu.:0.0000   3rd Qu.:12.25   Hazeltop  : 1  
+##  Max.   :1.0000      Max.   :0.5000   Max.   :16.00   Kukaklek  : 1  
+##                                                       (Other)   :10  
+##        SampleType         campaign         abrasion feldspar plagioclase
+##  atmospheric: 1   Crater Floor:9   Alfalfa     :2   0:14     0:13       
+##  regolith   : 0   Delta Front :7   Bellegarde  :2   1: 2     1: 3       
+##  rock core  :15   Margin Unit :0   Berry Hollow:2                       
+##                                    Dourbes     :2                       
+##                                    Novarupta   :2                       
+##                                    Quartier    :2                       
+##                                    (Other)     :4                       
+##  pyroxene olivine quartz apatite FeTi_Oxides Iron_Oxide Sulfate Perchlorates
+##  0: 5     0: 6    0:14   0:13    0:13        0:9        0: 4    0:15        
+##  1:11     1:10    1: 2   1: 3    1: 3        1:7        1:12    1: 1        
+##                                                                             
+##                                                                             
+##                                                                             
+##                                                                             
+##                                                                             
+##  Phosphate Ca_Sulfate Carbonate Fe_Mg_clay Fe_Mg_carbonate Mg_sulfate
+##  0:11      0:10       0: 1      0:13       0:14            0:13      
+##  1: 5      1: 6       1:15      1: 3       1: 2            1: 3      
+##                                                                      
+##                                                                      
+##                                                                      
+##                                                                      
+##                                                                      
+##  Phyllosilicates Chlorite Halite Organic_matter Hydrated_Ca_Sulfate
+##  0:12            0:14     0:13   0: 5           0:14               
+##  1: 4            1: 2     1: 3   1:11           1: 2               
+##                                                                    
+##                                                                    
+##                                                                    
+##                                                                    
+##                                                                    
+##  Hydrated_Sulfates Hydrated_Mg_Fe_Sulfate Na_Perchlorate Amorphous_Silicate
+##  0:14              0:13                   0:15           0:9               
+##  1: 2              1: 3                   1: 1           1:7               
+##                                                                            
+##                                                                            
+##                                                                            
+##                                                                            
+##                                                                            
+##  Hydrated_Carbonates Disordered_Silicates Hydrated_Iron_Oxide
+##  0:16                0:14                 0:15               
+##                      1: 2                 1: 1               
+##                                                              
+##                                                              
+##                                                              
+##                                                              
+##                                                              
+##  Sulfate+Organic_Matter Other_hydrated_phases Kaolinite Chromite Ilmenite
+##  0:11                   0:8                   0:13      0:14     0:14    
+##  1: 5                   1:8                   1: 3      1: 2     1: 2    
+##                                                                          
+##                                                                          
+##                                                                          
+##                                                                          
+##                                                                          
+##  Zircon/Baddeleyite Spinels
+##  0:14               0:14   
+##  1: 2               1: 2   
+##                            
+##                            
+##                            
+##                            
+## 
+
# Combine the Lithology and SHERLOC matrices
+sherloc_lithology.matrix<-cbind(sherloc.matrix,lithology.matrix)
+
+# Review the resulting matrix
+str(sherloc_lithology.matrix)
+
##  num [1:16, 1:70] 1 1 1 0 0 0 0 0 0 0 ...
+##  - attr(*, "dimnames")=List of 2
+##   ..$ : NULL
+##   ..$ : chr [1:70] "Plagioclase" "Sulfate" "Ca-sulfate" "Hydrated Ca-sulfate" ...
+
+
+

3.8 Data Set H: Sherloc + +Lithology + PIXL

+

Create data frame and matrix from prior datasets by making on +appropriate combinations.

+
# Combine the Lithology and SHERLOC dataframes
+sherloc_lithology_pixl.df <- cbind(sherloc.df,lithology.df, pixl.df )
+
+# Review what we have
+summary(sherloc_lithology_pixl.df)
+
##      sample               type           campaign         abrasion
+##  Min.   : 1.00   Igneous    :8   Crater Floor:9   Alfalfa     :2  
+##  1st Qu.: 4.75   N/A        :1   Delta Front :7   Bellegrade  :2  
+##  Median : 8.50   Sedimentary:7                    Berry Hollow:2  
+##  Mean   : 8.50                                    Dourbes     :2  
+##  3rd Qu.:12.25                                    Novarupta   :2  
+##  Max.   :16.00                                    Quartier    :2  
+##                                                   (Other)     :4  
+##          Name     Plagioclase        Sulfate         Ca-sulfate    
+##  Atsah     : 1   Min.   :0.0000   Min.   :0.0000   Min.   :0.0000  
+##  Bearwallow: 1   1st Qu.:0.0000   1st Qu.:0.1875   1st Qu.:0.0000  
+##  Coulettes : 1   Median :0.0000   Median :1.0000   Median :0.0000  
+##  Hahonih   : 1   Mean   :0.1875   Mean   :0.6562   Mean   :0.3438  
+##  Hazeltop  : 1   3rd Qu.:0.0000   3rd Qu.:1.0000   3rd Qu.:1.0000  
+##  Kukaklek  : 1   Max.   :1.0000   Max.   :1.0000   Max.   :1.0000  
+##  (Other)   :10                                                     
+##  Hydrated Ca-sulfate   Mg-sulfate     Hydrated Sulfates Hydrated Mg-Fe sulfate
+##  Min.   :0.000       Min.   :0.0000   Min.   :0.000     Min.   :0.0000        
+##  1st Qu.:0.000       1st Qu.:0.0000   1st Qu.:0.000     1st Qu.:0.0000        
+##  Median :0.000       Median :0.0000   Median :0.000     Median :0.0000        
+##  Mean   :0.125       Mean   :0.1875   Mean   :0.125     Mean   :0.1875        
+##  3rd Qu.:0.000       3rd Qu.:0.0000   3rd Qu.:0.000     3rd Qu.:0.0000        
+##  Max.   :1.000       Max.   :1.0000   Max.   :1.000     Max.   :1.0000        
+##                                                                               
+##   Perchlorates    Na-perchlorate    Amorphous Silicate   Phosphate     
+##  Min.   :0.0000   Min.   :0.00000   Min.   :0.0000     Min.   :0.0000  
+##  1st Qu.:0.0000   1st Qu.:0.00000   1st Qu.:0.0000     1st Qu.:0.0000  
+##  Median :0.0000   Median :0.00000   Median :0.0000     Median :0.0000  
+##  Mean   :0.0625   Mean   :0.03125   Mean   :0.1406     Mean   :0.2031  
+##  3rd Qu.:0.0000   3rd Qu.:0.00000   3rd Qu.:0.2500     3rd Qu.:0.3125  
+##  Max.   :1.0000   Max.   :0.50000   Max.   :0.5000     Max.   :1.0000  
+##                                                                        
+##     Pyroxene         Olivine         Carbonate      Fe-Mg carbonate
+##  Min.   :0.0000   Min.   :0.0000   Min.   :0.0000   Min.   :0.000  
+##  1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.4375   1st Qu.:0.000  
+##  Median :1.0000   Median :0.6250   Median :1.0000   Median :0.000  
+##  Mean   :0.6875   Mean   :0.5312   Mean   :0.7344   Mean   :0.125  
+##  3rd Qu.:1.0000   3rd Qu.:1.0000   3rd Qu.:1.0000   3rd Qu.:0.000  
+##  Max.   :1.0000   Max.   :1.0000   Max.   :1.0000   Max.   :1.000  
+##                                                                    
+##  Hydrated Carbonates Disordered Silicates    Feldspar         Quartz       
+##  Min.   :0           Min.   :0.000        Min.   :0.000   Min.   :0.00000  
+##  1st Qu.:0           1st Qu.:0.000        1st Qu.:0.000   1st Qu.:0.00000  
+##  Median :0           Median :0.000        Median :0.000   Median :0.00000  
+##  Mean   :0           Mean   :0.125        Mean   :0.125   Mean   :0.03125  
+##  3rd Qu.:0           3rd Qu.:0.000        3rd Qu.:0.000   3rd Qu.:0.00000  
+##  Max.   :0           Max.   :1.000        Max.   :1.000   Max.   :0.25000  
+##                                                                            
+##     Apatite        FeTi oxides         Halite          Iron oxide    
+##  Min.   :0.0000   Min.   :0.0000   Min.   :0.00000   Min.   :0.0000  
+##  1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.00000   1st Qu.:0.0000  
+##  Median :0.0000   Median :0.0000   Median :0.00000   Median :0.0000  
+##  Mean   :0.1406   Mean   :0.1406   Mean   :0.04688   Mean   :0.2812  
+##  3rd Qu.:0.0000   3rd Qu.:0.0000   3rd Qu.:0.00000   3rd Qu.:0.5000  
+##  Max.   :1.0000   Max.   :1.0000   Max.   :0.25000   Max.   :1.0000  
+##                                                                      
+##  Hydrated Iron oxide Organic matter   Sulfate+Organic matter
+##  Min.   :0.00000     Min.   :0.0000   Min.   :0.0000        
+##  1st Qu.:0.00000     1st Qu.:0.0000   1st Qu.:0.0000        
+##  Median :0.00000     Median :1.0000   Median :0.0000        
+##  Mean   :0.01562     Mean   :0.5938   Mean   :0.2188        
+##  3rd Qu.:0.00000     3rd Qu.:1.0000   3rd Qu.:0.2500        
+##  Max.   :0.25000     Max.   :1.0000   Max.   :1.0000        
+##                                                             
+##  Other hydrated phases Phyllosilicates      Chlorite     
+##  Min.   :0.0000        Min.   :0.00000   Min.   :0.0000  
+##  1st Qu.:0.0000        1st Qu.:0.00000   1st Qu.:0.0000  
+##  Median :0.2500        Median :0.00000   Median :0.0000  
+##  Mean   :0.4375        Mean   :0.09375   Mean   :0.0625  
+##  3rd Qu.:1.0000        3rd Qu.:0.06250   3rd Qu.:0.0000  
+##  Max.   :1.0000        Max.   :0.50000   Max.   :0.5000  
+##                                                          
+##  Kaolinite (hydrous Al-clay)    Chromite        Ilmenite     Zircon/Baddeleyite
+##  Min.   :0.0000              Min.   :0.000   Min.   :0.000   Min.   :0.000     
+##  1st Qu.:0.0000              1st Qu.:0.000   1st Qu.:0.000   1st Qu.:0.000     
+##  Median :0.0000              Median :0.000   Median :0.000   Median :0.000     
+##  Mean   :0.1875              Mean   :0.125   Mean   :0.125   Mean   :0.125     
+##  3rd Qu.:0.0000              3rd Qu.:0.000   3rd Qu.:0.000   3rd Qu.:0.000     
+##  Max.   :1.0000              Max.   :1.000   Max.   :1.000   Max.   :1.000     
+##                                                                                
+##  Fe-Mg-clay minerals    Spinels           sample              name   
+##  Min.   :0.0000      Min.   :0.0000   Min.   : 1.00   Atsah     : 1  
+##  1st Qu.:0.0000      1st Qu.:0.0000   1st Qu.: 4.75   Bearwallow: 1  
+##  Median :0.0000      Median :0.0000   Median : 8.50   Coulettes : 1  
+##  Mean   :0.1875      Mean   :0.0625   Mean   : 8.50   Hahonih   : 1  
+##  3rd Qu.:0.0000      3rd Qu.:0.0000   3rd Qu.:12.25   Hazeltop  : 1  
+##  Max.   :1.0000      Max.   :0.5000   Max.   :16.00   Kukaklek  : 1  
+##                                                       (Other)   :10  
+##        SampleType         campaign         abrasion feldspar plagioclase
+##  atmospheric: 1   Crater Floor:9   Alfalfa     :2   0:14     0:13       
+##  regolith   : 0   Delta Front :7   Bellegarde  :2   1: 2     1: 3       
+##  rock core  :15   Margin Unit :0   Berry Hollow:2                       
+##                                    Dourbes     :2                       
+##                                    Novarupta   :2                       
+##                                    Quartier    :2                       
+##                                    (Other)     :4                       
+##  pyroxene olivine quartz apatite FeTi_Oxides Iron_Oxide Sulfate Perchlorates
+##  0: 5     0: 6    0:14   0:13    0:13        0:9        0: 4    0:15        
+##  1:11     1:10    1: 2   1: 3    1: 3        1:7        1:12    1: 1        
+##                                                                             
+##                                                                             
+##                                                                             
+##                                                                             
+##                                                                             
+##  Phosphate Ca_Sulfate Carbonate Fe_Mg_clay Fe_Mg_carbonate Mg_sulfate
+##  0:11      0:10       0: 1      0:13       0:14            0:13      
+##  1: 5      1: 6       1:15      1: 3       1: 2            1: 3      
+##                                                                      
+##                                                                      
+##                                                                      
+##                                                                      
+##                                                                      
+##  Phyllosilicates Chlorite Halite Organic_matter Hydrated_Ca_Sulfate
+##  0:12            0:14     0:13   0: 5           0:14               
+##  1: 4            1: 2     1: 3   1:11           1: 2               
+##                                                                    
+##                                                                    
+##                                                                    
+##                                                                    
+##                                                                    
+##  Hydrated_Sulfates Hydrated_Mg_Fe_Sulfate Na_Perchlorate Amorphous_Silicate
+##  0:14              0:13                   0:15           0:9               
+##  1: 2              1: 3                   1: 1           1:7               
+##                                                                            
+##                                                                            
+##                                                                            
+##                                                                            
+##                                                                            
+##  Hydrated_Carbonates Disordered_Silicates Hydrated_Iron_Oxide
+##  0:16                0:14                 0:15               
+##                      1: 2                 1: 1               
+##                                                              
+##                                                              
+##                                                              
+##                                                              
+##                                                              
+##  Sulfate+Organic_Matter Other_hydrated_phases Kaolinite Chromite Ilmenite
+##  0:11                   0:8                   0:13      0:14     0:14    
+##  1: 5                   1:8                   1: 3      1: 2     1: 2    
+##                                                                          
+##                                                                          
+##                                                                          
+##                                                                          
+##                                                                          
+##  Zircon/Baddeleyite Spinels     sample           Na20            Mgo        
+##  0:14               0:14    Min.   : 1.00   Min.   :1.000   Min.   : 0.730  
+##  1: 2               1: 2    1st Qu.: 4.75   1st Qu.:1.853   1st Qu.: 2.533  
+##                             Median : 8.50   Median :1.900   Median :12.800  
+##                             Mean   : 8.50   Mean   :2.672   Mean   :11.682  
+##                             3rd Qu.:12.25   3rd Qu.:4.500   3rd Qu.:19.100  
+##                             Max.   :16.00   Max.   :5.550   Max.   :22.700  
+##                                                                             
+##      Al203             Si02            P205             S03        
+##  Min.   : 1.700   Min.   :22.60   Min.   :0.1000   Min.   : 0.780  
+##  1st Qu.: 2.220   1st Qu.:31.22   1st Qu.:0.2350   1st Qu.: 1.495  
+##  Median : 3.710   Median :38.85   Median :0.5250   Median : 2.600  
+##  Mean   : 5.072   Mean   :38.55   Mean   :0.6512   Mean   : 5.562  
+##  3rd Qu.: 7.117   3rd Qu.:41.17   3rd Qu.:0.8400   3rd Qu.: 3.800  
+##  Max.   :11.600   Max.   :57.10   Max.   :2.7600   Max.   :21.530  
+##                                                                    
+##        Cl             K20              Cao             Ti02       
+##  Min.   :0.400   Min.   :0.0000   Min.   :1.500   Min.   :0.2000  
+##  1st Qu.:0.940   1st Qu.:0.1600   1st Qu.:2.655   1st Qu.:0.5900  
+##  Median :1.740   Median :0.2000   Median :3.120   Median :0.7000  
+##  Mean   :1.846   Mean   :0.5800   Mean   :3.688   Mean   :0.8194  
+##  3rd Qu.:2.080   3rd Qu.:0.8275   3rd Qu.:4.310   3rd Qu.:0.9900  
+##  Max.   :4.500   Max.   :1.9000   Max.   :7.770   Max.   :2.4900  
+##                                                                   
+##      Cr203            Mno             FeO-T               name   
+##  Min.   :0.000   Min.   :0.1000   Min.   :13.24   Atsah     : 1  
+##  1st Qu.:0.025   1st Qu.:0.2800   1st Qu.:16.71   Bearwallow: 1  
+##  Median :0.155   Median :0.4000   Median :23.86   Coulettes : 1  
+##  Mean   :0.355   Mean   :0.3812   Mean   :21.45   Hahonih   : 1  
+##  3rd Qu.:0.290   3rd Qu.:0.4900   3rd Qu.:25.70   Hazeltop  : 1  
+##  Max.   :1.900   Max.   :0.6900   Max.   :30.05   Kukaklek  : 1  
+##                                                   (Other)   :10  
+##           type           campaign    location          abrasion
+##  Igneous    :8   Crater Floor:9   01     : 1   Alfalfa     :2  
+##  N/A        :1   Delta Front :7   02     : 1   Bellegrade  :2  
+##  Sedimentary:7                    03     : 1   Berry Hollow:2  
+##                                   04     : 1   Dourbes     :2  
+##                                   05     : 1   Novarupta   :2  
+##                                   06     : 1   Quartier    :2  
+##                                   (Other):10   (Other)     :4
+
# Combine the Lithology, SHERLOC and PIXLmatrices
+sherloc_lithology_pixl.matrix<-cbind(sherloc.matrix,lithology.matrix,pixl.matrix)
+
+# Review the resulting matrix
+str(sherloc_lithology_pixl.matrix)
+
##  num [1:16, 1:83] 1 1 1 0 0 0 0 0 0 0 ...
+##  - attr(*, "dimnames")=List of 2
+##   ..$ : NULL
+##   ..$ : chr [1:83] "Plagioclase" "Sulfate" "Ca-sulfate" "Hydrated Ca-sulfate" ...
+
+
+
+

4 Analysis of Data (Part +3)

+

Each team has been assigned one of six datasets:

+
    +
  1. Dataset B: PIXL: The PIXL team’s goal is to understand and +explain how scaling changes results from Assignment 1. The matrix +version was scaled above but not in Assignment 1.

  2. +
  3. Dataset C: LIBS (with appropriate scaling as necessary. Not +scaled yet.)

  4. +
  5. Dataset D: Sherloc (with appropriate scaling as necessary. Not +scaled yet.)

  6. +
  7. Dataset E: PIXL + Sherloc (with appropriate scaling as necessary. +Not scaled yet.)

  8. +
  9. Dataset F: PIXL + Lithography (with appropriate scaling as +necessary. Not scaled yet.)

  10. +
  11. Dataset G: Sherloc + Lithograpy (with appropriate scaling as +necessary. Not scaled yet.)

  12. +
  13. Dataset H: PIXL + Sherloc + Lithograpy (with appropriate scaling +as necessary. Not scaled yet.)

  14. +
+

For the data set assigned to your team, perform the following +steps. Feel free to use the methods/code from Assignment 1 as +desired. Communicate with your teammates. Make sure that you are doing +different variations of below analysis so that no team member does the +exact same analysis. If you want to use the same clustering for your +team (which is okay but then vary rest), make sure you use the same +random seeds.

+
    +
  1. Describe the data set contained in the data frame and +matrix: How many rows does it have and how many features? Which +features are measurements and which features are metadata about the +samples? (3 pts)

  2. +
  3. Scale this data appropriately (you can choose the scaling +method or decide to not scale data): Explain why you chose a +scaling method or to not scale. (3 pts)

  4. +
  5. Cluster the data using k-means or your favorite clustering +method (like hierarchical clustering): Describe how you picked the +best number of clusters. Indicate the number of points in each clusters. +Coordinate with your team so you try different approaches. If you want +to share results with your team mates, make sure to use the same random +seeds. (6 pts)

  6. +
  7. _Perform a creative analysis that provides +insights into what one or more of the clusters are and what they tell +you about the MARS data: Alternatively do another creative analysis of +your datasets that leads to one of more findings. Make sure to explain +what your analysis and discuss your the results.

  8. +
+
+
+

5 Preparation of Team +Presentation (Part 4)

+

Prepare a presentation of your teams result to present in class on +September 11 starting at 9am in AE217 (20 pts) The +presentation should include the following elements

+

0.Your teams names and members 1. A Description of +the data set that you analyzed including how many observations and how +many features. (<= 1.5 mins) 2. Each team member gets three +minutes to explain their analysis: * what analysis they +performed * the results of that analysis * a brief discussion of their +interpretation of these results * <= 18 mins total! 3. A +Conclusion slide indicating major findings of the teams +(<= 1.5 mins) 4. Thoughts on potential next steps +for the MARS team (<= 1.5 mins)

+ +

https://docs.google.com/document/d/1-4o1O4h2r8aMjAplmE-ItblQnyDAKZwNs5XCnmwacjs/pub

+
    +
  • Post a link to your teams presentation in the MARS webex chat before +class. You can continue to edit until the last minute.
  • +
+
+
+

6 When you’re done: SAVE, +COMMIT and PUSH YOUR CHANGES!

+

When you are satisfied with your edits and your notebook knits +successfully, remember to push your changes to the repo using the +following steps:

+
    +
  • git branch +
      +
    • To double-check that you are in your working branch
    • +
  • +
  • git add <your changed files>
  • +
  • git commit -m "Some useful comments"
  • +
  • git push origin <your branch name>
  • +
  • do a pull request
  • +
+
+
+

7 APPENDIX: Accessing +RStudio Server on the IDEA Cluster

+

The IDEA Cluster provides seven compute nodes (4x 48 cores, 3x 80 +cores, 1x storage server)

+
    +
  • The Cluster requires RCS credentials, enabled via registration in +class +
      +
    • email John Erickson for problems erickj4@rpi.edu
    • +
  • +
  • RStudio, Jupyter, MATLAB, GPUs (on two nodes); lots of storage and +computes
  • +
  • Access via RPI physical network or VPN only
  • +
+
+
+

8 More info about Rstudio +on our Cluster

+
+

8.1 RStudio GUI +Access:

+ +
+
+ + + + +
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a/StudentNotebooks/Assignment02/zhaot4-f24-assignment2.Rmd b/StudentNotebooks/Assignment02/zhaot4-f24-assignment2.Rmd index d087ce4..e648a2e 100644 --- a/StudentNotebooks/Assignment02/zhaot4-f24-assignment2.Rmd +++ b/StudentNotebooks/Assignment02/zhaot4-f24-assignment2.Rmd @@ -386,13 +386,111 @@ Each team has been assigned one of six datasets: **For the data set assigned to your team, perform the following steps.** Feel free to use the methods/code from Assignment 1 as desired. Communicate with your teammates. Make sure that you are doing different variations of below analysis so that no team member does the exact same analysis. If you want to use the same clustering for your team (which is okay but then vary rest), make sure you use the same random seeds. 1. _Describe the data set contained in the data frame and matrix:_ How many rows does it have and how many features? Which features are measurements and which features are metadata about the samples? (3 pts) +There is 16 rows and 80 features. min, max, mean, median, 1st qu, 3rd qu are measurements, and 2. _Scale this data appropriately (you can choose the scaling method or decide to not scale data):_ Explain why you chose a scaling method or to not scale. (3 pts) +Since the dataset contains both numerical and categorical features, I decide to not scale the data since scaling categorical variables can result in meaningless transformations. 3. _Cluster the data using k-means or your favorite clustering method (like hierarchical clustering):_ Describe how you picked the best number of clusters. Indicate the number of points in each clusters. Coordinate with your team so you try different approaches. If you want to share results with your team mates, make sure to use the same random seeds. (6 pts) 4. _Perform a **creative analysis** that provides insights into what one or more of the clusters are and what they tell you about the MARS data: Alternatively do another creative analysis of your datasets that leads to one of more findings. Make sure to explain what your analysis and discuss your the results. +```{r} +sherloc_lithology.matrix[is.na(sherloc_lithology.matrix)] <- mean(sherloc_lithology.matrix, na.rm = TRUE) +scaled_data <- scale(sherloc_lithology.matrix) + +``` + + +```{r} +dim(sherloc_lithology.df) + + +# A user-defined function to examine clusters and plot the results +wssplot <- function(data, nc=15, seed=10){ + wss <- data.frame(cluster=1:nc, quality=c(0)) + for (i in 1:nc){ + set.seed(seed) + wss[i,2] <- kmeans(data, centers=i)$tot.withinss} + ggplot(data=wss,aes(x=cluster,y=quality)) + + geom_line() + + ggtitle("Quality of k-means by Cluster") +} + +wssplot(sherloc_lithology.matrix, nc=8, seed=2) +``` + +Create final clusters +```{r} +# Use our chosen 'k' to perform k-means clustering +set.seed(2) +k <- 3 +km <- kmeans(sherloc_lithology.matrix,k) +``` + +At first, we keep the scale as the origin, and create a heat map of the cluster centers with rows and columns clustered. +```{r} +pheatmap(km$centers,scale="none") +``` +According to this heat map, the features at left have a high mean than the features at right. Moreover, cluster 2 has an over all more high mean than cluster 1 and cluster 3. + +Now, performing PCA. +```{r} +# Perform the PCA on the matrix we created earlier + +sherloc_lithology.pca <- prcomp(sherloc_lithology.matrix, scale=FALSE) + +# generate the Scree plot +ggscreeplot(sherloc_lithology.pca) +``` + +Next, indicating how many samples are in each cluster +```{r} +library(knitr) +# clusters sizes are in the km object produced by kmeans +clusters.df<-data.frame(cluster= 1:3, size=km$size) +kable(clusters.df,caption="Samples per cluster") +``` +Creative analysis: +```{r} +summary(sherloc_lithology.pca) + +# Plotting the variance explained by each principal component +plot(sherloc_lithology.pca, type="l") +``` +Together, the first three components explain about 70.48% of the variance.This means that using the first three components might provide a good approximation of the dataset, significantly reducing its dimensionality while retaining most of the important information. +Elbow Rule: The plot shows a clear "elbow" around the 3rd or 4th component. After this point, the variance explained by each additional component drops off significantly. +Based on this scree plot, the first 3-4 principal components should be considered for further analysis, as they explain the majority of the variance in the dataset. After the 4th component, the additional variance explained becomes minimal. + + +```{r} +loadings <- sherloc_lithology.pca$rotation[,1:4] +print(loadings) +``` +Based on the result, SHERLOC measurements dominate PC1 and lithology measurements dominate PC2, we could infer that PC1 captures the primary chemical or spectroscopic composition of the Martian surface, while PC2 relates to the geological context. + +Create a PCA biplot to visualize the clusters +```{r} +# For this lab we'll create a PCA biplot the easy way using ggbiplot! +ggbiplot::ggbiplot(sherloc_lithology.pca, + choices = c(1,2), + labels = sherloc_lithology.df$type, + groups = as.factor(km$cluster)) + + xlim(-2,2) + ylim(-2,2) +``` + +make another PCA biplot to create a comparison between PC1 and PC3 +```{r} +ggbiplot::ggbiplot(sherloc_lithology.pca, + choices = c(1,3), + labels = sherloc_lithology.df$type, + groups = as.factor(km$cluster)) + + xlim(-2,2) + ylim(-2,2) + +``` + + + # Preparation of Team Presentation (Part 4) diff --git a/StudentNotebooks/Assignment02/zhaot4-f24-assignment2.html b/StudentNotebooks/Assignment02/zhaot4-f24-assignment2.html index 555d612..0408f65 100644 --- a/StudentNotebooks/Assignment02/zhaot4-f24-assignment2.html +++ b/StudentNotebooks/Assignment02/zhaot4-f24-assignment2.html @@ -11,7 +11,7 @@ - + Mars 2020 Mission Data Notebook-zhaot4: @@ -1625,7 +1625,7 @@

Mars 2020 Mission Data Notebook-zhaot4:

Mars DAR Assignment 2 (Fall 2024)

Tianhao Zhao

-

04 September 2024

+

07 September 2024

@@ -2925,10 +2925,14 @@

4 Analysis of Data (Part
  • Describe the data set contained in the data frame and matrix: How many rows does it have and how many features? Which features are measurements and which features are metadata about the -samples? (3 pts)

  • +samples? (3 pts) There is 16 rows and 80 features. min, max, mean, +median, 1st qu, 3rd qu are measurements, and

  • Scale this data appropriately (you can choose the scaling method or decide to not scale data): Explain why you chose a -scaling method or to not scale. (3 pts)

  • +scaling method or to not scale. (3 pts) Since the dataset contains both +numerical and categorical features, I decide to not scale the data since +scaling categorical variables can result in meaningless +transformations.

  • Cluster the data using k-means or your favorite clustering method (like hierarchical clustering): Describe how you picked the best number of clusters. Indicate the number of points in each clusters. @@ -2941,6 +2945,198 @@

    4 Analysis of Data (Part your datasets that leads to one of more findings. Make sure to explain what your analysis and discuss your the results.

  • +
    sherloc_lithology.matrix[is.na(sherloc_lithology.matrix)] <- mean(sherloc_lithology.matrix, na.rm = TRUE)
    +scaled_data <- scale(sherloc_lithology.matrix)
    +
    dim(sherloc_lithology.df)
    +
    ## [1] 16 80
    +
    # A user-defined function to examine clusters and plot the results
    +wssplot <- function(data, nc=15, seed=10){
    +  wss <- data.frame(cluster=1:nc, quality=c(0))
    +  for (i in 1:nc){
    +    set.seed(seed)
    +    wss[i,2] <- kmeans(data, centers=i)$tot.withinss}
    +  ggplot(data=wss,aes(x=cluster,y=quality)) + 
    +    geom_line() + 
    +    ggtitle("Quality of k-means by Cluster")
    +}
    +
    +wssplot(sherloc_lithology.matrix, nc=8, seed=2)
    +

    +

    Create final clusters

    +
    # Use our chosen 'k' to perform k-means clustering
    +set.seed(2)
    +k <- 3
    +km <- kmeans(sherloc_lithology.matrix,k)
    +

    At first, we keep the scale as the origin, and create a heat map of +the cluster centers with rows and columns clustered.

    +
    pheatmap(km$centers,scale="none")
    +

    +According to this heat map, the features at left have a high mean than +the features at right. Moreover, cluster 2 has an over all more high +mean than cluster 1 and cluster 3.

    +

    Now, performing PCA.

    +
    # Perform the PCA on the matrix we created earlier
    +
    +sherloc_lithology.pca <- prcomp(sherloc_lithology.matrix, scale=FALSE)
    +
    +# generate the Scree plot
    +ggscreeplot(sherloc_lithology.pca)
    +

    +

    Next, indicating how many samples are in each cluster

    +
    library(knitr)
    +# clusters sizes are in the km object produced by kmeans
    +clusters.df<-data.frame(cluster= 1:3, size=km$size)
    +kable(clusters.df,caption="Samples per cluster")
    + + + + + + + + + + + + + + + + + + + + + + +
    Samples per cluster
    clustersize
    17
    22
    37
    +

    Creative analysis:

    +
    summary(sherloc_lithology.pca)
    +
    ## Importance of components:
    +##                           PC1    PC2    PC3    PC4     PC5     PC6     PC7
    +## Standard deviation     1.6370 1.5095 1.3427 1.1118 0.88099 0.70792 0.52226
    +## Proportion of Variance 0.2793 0.2375 0.1879 0.1289 0.08091 0.05224 0.02843
    +## Cumulative Proportion  0.2793 0.5169 0.7048 0.8337 0.91458 0.96682 0.99526
    +##                            PC8       PC9     PC10      PC11     PC12      PC13
    +## Standard deviation     0.21330 2.894e-16 1.79e-16 1.175e-16 9.92e-17 6.478e-17
    +## Proportion of Variance 0.00474 0.000e+00 0.00e+00 0.000e+00 0.00e+00 0.000e+00
    +## Cumulative Proportion  1.00000 1.000e+00 1.00e+00 1.000e+00 1.00e+00 1.000e+00
    +##                             PC14      PC15      PC16
    +## Standard deviation     4.869e-17 1.972e-17 2.379e-18
    +## Proportion of Variance 0.000e+00 0.000e+00 0.000e+00
    +## Cumulative Proportion  1.000e+00 1.000e+00 1.000e+00
    +
    # Plotting the variance explained by each principal component
    +plot(sherloc_lithology.pca, type="l")
    +

    +Together, the first three components explain about 70.48% of the +variance.This means that using the first three components might provide +a good approximation of the dataset, significantly reducing its +dimensionality while retaining most of the important information. Elbow +Rule: The plot shows a clear “elbow” around the 3rd or 4th component. +After this point, the variance explained by each additional component +drops off significantly. Based on this scree plot, the first 3-4 +principal components should be considered for further analysis, as they +explain the majority of the variance in the dataset. After the 4th +component, the additional variance explained becomes minimal.

    +
    loadings <- sherloc_lithology.pca$rotation[,1:4]
    +print(loadings)
    +
    ##                                      PC1          PC2          PC3          PC4
    +## Plagioclase                 -0.064336916  0.253285711  0.034736225  0.011964995
    +## Sulfate                     -0.175146396  0.057235074 -0.031239837  0.302918236
    +## Ca-sulfate                  -0.232159520  0.167134575 -0.064154734 -0.021631913
    +## Hydrated Ca-sulfate         -0.042131612  0.170024387  0.021970393  0.023568451
    +## Mg-sulfate                  -0.200670557 -0.107436782 -0.114769312 -0.033532288
    +## Hydrated Sulfates            0.046640374 -0.046533930  0.004709232  0.211811697
    +## Hydrated Mg-Fe sulfate      -0.200670557 -0.107436782 -0.114769312 -0.033532288
    +## Perchlorates                -0.022205304  0.083261324  0.012765831 -0.011603456
    +## Na-perchlorate              -0.011102652  0.041630662  0.006382916 -0.005801728
    +## Amorphous Silicate           0.017782440  0.039123645  0.003335076  0.124303014
    +## Phosphate                   -0.050067834  0.156937069  0.139435041 -0.027420114
    +## Pyroxene                     0.205440349  0.175242080 -0.113777068  0.129707690
    +## Olivine                      0.199073864 -0.131670868  0.156241523  0.150758082
    +## Carbonate                    0.128752482  0.006768303  0.124116776  0.122879865
    +## Fe-Mg carbonate              0.090812262  0.012522980 -0.038558702 -0.058532299
    +## Hydrated Carbonates          0.000000000  0.000000000  0.000000000  0.000000000
    +## Disordered Silicates         0.087911478 -0.018904080 -0.101611247 -0.172254385
    +## Feldspar                     0.087911478 -0.018904080 -0.101611247 -0.172254385
    +## Quartz                       0.021977870 -0.004726020 -0.025402812 -0.043063596
    +## Apatite                     -0.010321118 -0.046989967  0.231737838 -0.099076266
    +## FeTi oxides                 -0.047682938  0.190839718  0.025161851  0.020667587
    +## Halite                       0.017151739  0.023946076 -0.006448218 -0.017533939
    +## Iron oxide                   0.002321888  0.246964416 -0.025709074 -0.088795272
    +## Hydrated Iron oxide         -0.005551326  0.020815331  0.003191458 -0.002900864
    +## Organic matter              -0.022898001 -0.214954717 -0.167587308  0.118698855
    +## Sulfate+Organic matter      -0.020247980 -0.106056547  0.030089121  0.187897087
    +## Other hydrated phases        0.225821526 -0.068591591 -0.097707669  0.203869887
    +## Phyllosilicates              0.066658805 -0.006321295 -0.060445299 -0.100760267
    +## Chlorite                     0.043955739 -0.009452040 -0.050805623 -0.086127193
    +## Kaolinite (hydrous Al-clay) -0.200670557 -0.107436782 -0.114769312 -0.033532288
    +## Chromite                    -0.004769792 -0.067805298  0.228546380 -0.096175402
    +## Ilmenite                    -0.004769792 -0.067805298  0.228546380 -0.096175402
    +## Zircon/Baddeleyite          -0.004769792 -0.067805298  0.228546380 -0.096175402
    +## Fe-Mg-clay minerals         -0.200670557 -0.107436782 -0.114769312 -0.033532288
    +## Spinels                     -0.002384896 -0.033902649  0.114273190 -0.048087701
    +## feldspar                     0.087911478 -0.018904080 -0.101611247 -0.172254385
    +## plagioclase                 -0.064336916  0.253285711  0.034736225  0.011964995
    +## pyroxene                     0.205440349  0.175242080 -0.113777068  0.129707690
    +## olivine                      0.265007473 -0.145848928  0.080033088  0.021567293
    +## quartz                       0.087911478 -0.018904080 -0.101611247 -0.172254385
    +## apatite                     -0.026975096  0.015456026  0.241312212 -0.107778858
    +## FeTi_Oxides                 -0.064336916  0.253285711  0.034736225  0.011964995
    +## Iron_Oxide                   0.114386824  0.246904610 -0.105433723 -0.218821689
    +## Sulfate                     -0.178723740  0.006381100  0.140169948  0.230786684
    +## Perchlorates                -0.022205304  0.083261324  0.012765831 -0.011603456
    +## Phosphate                   -0.069106708  0.185480413  0.263282605 -0.084210407
    +## Ca_Sulfate                  -0.265007473  0.145848928 -0.080033088 -0.021567293
    +## Carbonate                    0.022205304 -0.083261324 -0.012765831  0.011603456
    +## Fe_Mg_clay                  -0.200670557 -0.107436782 -0.114769312 -0.033532288
    +## Fe_Mg_carbonate              0.090812262  0.012522980 -0.038558702 -0.058532299
    +## Mg_sulfate                  -0.200670557 -0.107436782 -0.114769312 -0.033532288
    +## Phyllosilicates              0.178723740 -0.006381100 -0.140169948 -0.230786684
    +## Chlorite                     0.087911478 -0.018904080 -0.101611247 -0.172254385
    +## Halite                       0.068606958  0.095784304 -0.025792870 -0.070135755
    +## Organic_matter              -0.026475345 -0.265808691  0.003822477  0.046567303
    +## Hydrated_Ca_Sulfate         -0.042131612  0.170024387  0.021970393  0.023568451
    +## Hydrated_Sulfates            0.046640374 -0.046533930  0.004709232  0.211811697
    +## Hydrated_Mg_Fe_Sulfate      -0.200670557 -0.107436782 -0.114769312 -0.033532288
    +## Na_Perchlorate              -0.022205304  0.083261324  0.012765831 -0.011603456
    +## Amorphous_Silicate           0.026716609  0.181623180  0.026392880  0.360494374
    +## Hydrated_Carbonates          0.000000000  0.000000000  0.000000000  0.000000000
    +## Disordered_Silicates         0.087911478 -0.018904080 -0.101611247 -0.172254385
    +## Hydrated_Iron_Oxide         -0.022205304  0.083261324  0.012765831 -0.011603456
    +## Sulfate+Organic_Matter      -0.023825324 -0.156910520  0.201498906  0.115765536
    +## Other_hydrated_phases        0.269777265 -0.078043631 -0.148513293  0.117742695
    +## Kaolinite                   -0.200670557 -0.107436782 -0.114769312 -0.033532288
    +## Chromite                    -0.004769792 -0.067805298  0.228546380 -0.096175402
    +## Ilmenite                    -0.004769792 -0.067805298  0.228546380 -0.096175402
    +## Zircon/Baddeleyite          -0.004769792 -0.067805298  0.228546380 -0.096175402
    +## Spinels                     -0.004769792 -0.067805298  0.228546380 -0.096175402
    +

    Based on the result, SHERLOC measurements dominate PC1 and lithology +measurements dominate PC2, we could infer that PC1 captures the primary +chemical or spectroscopic composition of the Martian surface, while PC2 +relates to the geological context.

    +

    Create a PCA biplot to visualize the clusters

    +
    # For this lab we'll create a PCA biplot the easy way using ggbiplot!
    +ggbiplot::ggbiplot(sherloc_lithology.pca,
    +                   choices = c(1,2),
    +                   labels = sherloc_lithology.df$type,
    +                   groups = as.factor(km$cluster)) +
    +  xlim(-2,2) + ylim(-2,2) 
    +
    ## Warning: Removed 2 rows containing missing values or values outside the scale range
    +## (`geom_text()`).
    +

    +

    make another PCA biplot to create a comparison between PC1 and +PC3

    +
    ggbiplot::ggbiplot(sherloc_lithology.pca,
    +                   choices = c(1,3),
    +                   labels = sherloc_lithology.df$type,
    +                   groups = as.factor(km$cluster)) +
    +  xlim(-2,2) + ylim(-2,2) 
    +
    ## Warning: Removed 2 rows containing missing values or values outside the scale range
    +## (`geom_text()`).
    +## Removed 2 rows containing missing values or values outside the scale range
    +## (`geom_text()`).
    +

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    Mars 2020 Mission Data Notebook-zhaot4:

    Mars DAR Assignment 2 (Fall 2024)

    Tianhao Zhao

    -

    07 September 2024

    +

    09 September 2024

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deletions(-) diff --git a/StudentNotebooks/Assignment02/zhaot4-f24-assignment2.Rmd b/StudentNotebooks/Assignment02/zhaot4-f24-assignment2.Rmd index e648a2e..406fb80 100644 --- a/StudentNotebooks/Assignment02/zhaot4-f24-assignment2.Rmd +++ b/StudentNotebooks/Assignment02/zhaot4-f24-assignment2.Rmd @@ -386,26 +386,21 @@ Each team has been assigned one of six datasets: **For the data set assigned to your team, perform the following steps.** Feel free to use the methods/code from Assignment 1 as desired. Communicate with your teammates. Make sure that you are doing different variations of below analysis so that no team member does the exact same analysis. If you want to use the same clustering for your team (which is okay but then vary rest), make sure you use the same random seeds. 1. _Describe the data set contained in the data frame and matrix:_ How many rows does it have and how many features? Which features are measurements and which features are metadata about the samples? (3 pts) -There is 16 rows and 80 features. min, max, mean, median, 1st qu, 3rd qu are measurements, and +There is 16 rows and 70 features. min, max, mean, median, 1st qu, 3rd qu are measurements, and + +```{r} +summary(sherloc_lithology.df) +str(sherloc_lithology.matrix) +``` 2. _Scale this data appropriately (you can choose the scaling method or decide to not scale data):_ Explain why you chose a scaling method or to not scale. (3 pts) Since the dataset contains both numerical and categorical features, I decide to not scale the data since scaling categorical variables can result in meaningless transformations. 3. _Cluster the data using k-means or your favorite clustering method (like hierarchical clustering):_ Describe how you picked the best number of clusters. Indicate the number of points in each clusters. Coordinate with your team so you try different approaches. If you want to share results with your team mates, make sure to use the same random seeds. (6 pts) +After darwing the wss plot of the matrix, I use elbow method plot to decide the best number of clusters. In this case, The elbow appears to form around 3 or 4 clusters. The sharp drop in the WCSS from 2 clusters to 3 clusters suggests that adding a third cluster significantly improves the clustering quality. Therefore, I choose 3 clusters. The first cluster has 7 points, the second cluster has 2 points and the third cluster has 7 points. -4. _Perform a **creative analysis** that provides insights into what one or more of the clusters are and what they tell you about the MARS data: Alternatively do another creative analysis of your datasets that leads to one of more findings. Make sure to explain what your analysis and discuss your the results. - -```{r} -sherloc_lithology.matrix[is.na(sherloc_lithology.matrix)] <- mean(sherloc_lithology.matrix, na.rm = TRUE) -scaled_data <- scale(sherloc_lithology.matrix) - -``` - - +CLustering ```{r} -dim(sherloc_lithology.df) - - # A user-defined function to examine clusters and plot the results wssplot <- function(data, nc=15, seed=10){ wss <- data.frame(cluster=1:nc, quality=c(0)) @@ -434,6 +429,15 @@ pheatmap(km$centers,scale="none") ``` According to this heat map, the features at left have a high mean than the features at right. Moreover, cluster 2 has an over all more high mean than cluster 1 and cluster 3. +Next, indicating how many samples are in each cluster +```{r} +library(knitr) +# clusters sizes are in the km object produced by kmeans +clusters.df<-data.frame(cluster= 1:3, size=km$size) +kable(clusters.df,caption="Samples per cluster") +``` + +4. _Perform a **creative analysis** that provides insights into what one or more of the clusters are and what they tell you about the MARS data: Alternatively do another creative analysis of your datasets that leads to one of more findings. Make sure to explain what your analysis and discuss your the results. Now, performing PCA. ```{r} # Perform the PCA on the matrix we created earlier @@ -444,13 +448,6 @@ sherloc_lithology.pca <- prcomp(sherloc_lithology.matrix, scale=FALSE) ggscreeplot(sherloc_lithology.pca) ``` -Next, indicating how many samples are in each cluster -```{r} -library(knitr) -# clusters sizes are in the km object produced by kmeans -clusters.df<-data.frame(cluster= 1:3, size=km$size) -kable(clusters.df,caption="Samples per cluster") -``` Creative analysis: ```{r} summary(sherloc_lithology.pca) @@ -464,31 +461,42 @@ Based on this scree plot, the first 3-4 principal components should be considere ```{r} -loadings <- sherloc_lithology.pca$rotation[,1:4] +loadings <- abs(sherloc_lithology.pca$rotation[, 1:3]) print(loadings) +threshold <- 0.2 +important_vars <- apply(loadings, 1, function(x) any(x > threshold)) +sherloc_lithology_filtered <- sherloc_lithology.pca +sherloc_lithology_filtered$rotation <- sherloc_lithology_filtered$rotation[important_vars, ] ``` +Using loading to show how much each variable contributes to the principal components. Then, I filtered the variables which only keep the variables that has a contribution greater than 0.2. +The high positive or negative values in the loading are most important to each component Based on the result, SHERLOC measurements dominate PC1 and lithology measurements dominate PC2, we could infer that PC1 captures the primary chemical or spectroscopic composition of the Martian surface, while PC2 relates to the geological context. Create a PCA biplot to visualize the clusters ```{r} # For this lab we'll create a PCA biplot the easy way using ggbiplot! -ggbiplot::ggbiplot(sherloc_lithology.pca, - choices = c(1,2), +ggbiplot::ggbiplot(sherloc_lithology_filtered, + choices = c(1, 2), labels = sherloc_lithology.df$type, groups = as.factor(km$cluster)) + - xlim(-2,2) + ylim(-2,2) + xlim(-2, 2) + ylim(-2, 2) + + ggtitle("Filtered Biplot: PC1 vs PC2") ``` +Iron Oxide, Amorphous Silicate, Pyroxene, Olivine, Hydrated Sulfates: These variables contribute the most to PC1, suggesting that PC1 continues to represent a contrast between igneous materials (e.g., pyroxene, olivine) and sedimentary or hydrated minerals (e.g., hydrated sulfates). Moreover, as these variables group closely together, which indicates a common geological origin. This likely corresponds to igneous regions on Mars +Phyllosilicates and Iron Oxide: These variables are also significant contributors to PC2, meaning PC2 is likely to represent variations within sedimentary environments which separate different types of hydrated minerals and phyllosilicates. This could reflect differences in the extent or type of chemical alteration due to water. + make another PCA biplot to create a comparison between PC1 and PC3 ```{r} -ggbiplot::ggbiplot(sherloc_lithology.pca, - choices = c(1,3), +ggbiplot::ggbiplot(sherloc_lithology_filtered, + choices = c(1, 3), labels = sherloc_lithology.df$type, groups = as.factor(km$cluster)) + - xlim(-2,2) + ylim(-2,2) + xlim(-2, 2) + ylim(-2, 2) + + ggtitle("Filtered Biplot: PC1 vs PC3") ``` - +Organic Matter and Phosphate: These variables are much more important in PC3 than PC2, suggesting that PC3 may capture some trend related to the presence of organic compounds or chemical processes that differ from those driving the first two PCs, distinguishing areas where organic compounds or specific chemical interactions are more prevalent. diff --git a/StudentNotebooks/Assignment02/zhaot4-f24-assignment2.html b/StudentNotebooks/Assignment02/zhaot4-f24-assignment2.html index 0408f65..88ef6c7 100644 --- a/StudentNotebooks/Assignment02/zhaot4-f24-assignment2.html +++ b/StudentNotebooks/Assignment02/zhaot4-f24-assignment2.html @@ -11,7 +11,7 @@ - + Mars 2020 Mission Data Notebook-zhaot4: @@ -1625,7 +1625,7 @@

    @@ -2922,11 +2922,171 @@

    4 Analysis of Data (Part team (which is okay but then vary rest), make sure you use the same random seeds.

      -
    1. Describe the data set contained in the data frame and +

    2. Describe the data set contained in the data frame and matrix: How many rows does it have and how many features? Which features are measurements and which features are metadata about the -samples? (3 pts) There is 16 rows and 80 features. min, max, mean, -median, 1st qu, 3rd qu are measurements, and

    3. +samples? (3 pts) There is 16 rows and 70 features. min, max, mean, +median, 1st qu, 3rd qu are measurements, and +
    +
    summary(sherloc_lithology.df)
    +
    ##      sample               type           campaign         abrasion
    +##  Min.   : 1.00   Igneous    :8   Crater Floor:9   Alfalfa     :2  
    +##  1st Qu.: 4.75   N/A        :1   Delta Front :7   Bellegrade  :2  
    +##  Median : 8.50   Sedimentary:7                    Berry Hollow:2  
    +##  Mean   : 8.50                                    Dourbes     :2  
    +##  3rd Qu.:12.25                                    Novarupta   :2  
    +##  Max.   :16.00                                    Quartier    :2  
    +##                                                   (Other)     :4  
    +##          Name     Plagioclase        Sulfate         Ca-sulfate    
    +##  Atsah     : 1   Min.   :0.0000   Min.   :0.0000   Min.   :0.0000  
    +##  Bearwallow: 1   1st Qu.:0.0000   1st Qu.:0.1875   1st Qu.:0.0000  
    +##  Coulettes : 1   Median :0.0000   Median :1.0000   Median :0.0000  
    +##  Hahonih   : 1   Mean   :0.1875   Mean   :0.6562   Mean   :0.3438  
    +##  Hazeltop  : 1   3rd Qu.:0.0000   3rd Qu.:1.0000   3rd Qu.:1.0000  
    +##  Kukaklek  : 1   Max.   :1.0000   Max.   :1.0000   Max.   :1.0000  
    +##  (Other)   :10                                                     
    +##  Hydrated Ca-sulfate   Mg-sulfate     Hydrated Sulfates Hydrated Mg-Fe sulfate
    +##  Min.   :0.000       Min.   :0.0000   Min.   :0.000     Min.   :0.0000        
    +##  1st Qu.:0.000       1st Qu.:0.0000   1st Qu.:0.000     1st Qu.:0.0000        
    +##  Median :0.000       Median :0.0000   Median :0.000     Median :0.0000        
    +##  Mean   :0.125       Mean   :0.1875   Mean   :0.125     Mean   :0.1875        
    +##  3rd Qu.:0.000       3rd Qu.:0.0000   3rd Qu.:0.000     3rd Qu.:0.0000        
    +##  Max.   :1.000       Max.   :1.0000   Max.   :1.000     Max.   :1.0000        
    +##                                                                               
    +##   Perchlorates    Na-perchlorate    Amorphous Silicate   Phosphate     
    +##  Min.   :0.0000   Min.   :0.00000   Min.   :0.0000     Min.   :0.0000  
    +##  1st Qu.:0.0000   1st Qu.:0.00000   1st Qu.:0.0000     1st Qu.:0.0000  
    +##  Median :0.0000   Median :0.00000   Median :0.0000     Median :0.0000  
    +##  Mean   :0.0625   Mean   :0.03125   Mean   :0.1406     Mean   :0.2031  
    +##  3rd Qu.:0.0000   3rd Qu.:0.00000   3rd Qu.:0.2500     3rd Qu.:0.3125  
    +##  Max.   :1.0000   Max.   :0.50000   Max.   :0.5000     Max.   :1.0000  
    +##                                                                        
    +##     Pyroxene         Olivine         Carbonate      Fe-Mg carbonate
    +##  Min.   :0.0000   Min.   :0.0000   Min.   :0.0000   Min.   :0.000  
    +##  1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.4375   1st Qu.:0.000  
    +##  Median :1.0000   Median :0.6250   Median :1.0000   Median :0.000  
    +##  Mean   :0.6875   Mean   :0.5312   Mean   :0.7344   Mean   :0.125  
    +##  3rd Qu.:1.0000   3rd Qu.:1.0000   3rd Qu.:1.0000   3rd Qu.:0.000  
    +##  Max.   :1.0000   Max.   :1.0000   Max.   :1.0000   Max.   :1.000  
    +##                                                                    
    +##  Hydrated Carbonates Disordered Silicates    Feldspar         Quartz       
    +##  Min.   :0           Min.   :0.000        Min.   :0.000   Min.   :0.00000  
    +##  1st Qu.:0           1st Qu.:0.000        1st Qu.:0.000   1st Qu.:0.00000  
    +##  Median :0           Median :0.000        Median :0.000   Median :0.00000  
    +##  Mean   :0           Mean   :0.125        Mean   :0.125   Mean   :0.03125  
    +##  3rd Qu.:0           3rd Qu.:0.000        3rd Qu.:0.000   3rd Qu.:0.00000  
    +##  Max.   :0           Max.   :1.000        Max.   :1.000   Max.   :0.25000  
    +##                                                                            
    +##     Apatite        FeTi oxides         Halite          Iron oxide    
    +##  Min.   :0.0000   Min.   :0.0000   Min.   :0.00000   Min.   :0.0000  
    +##  1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.00000   1st Qu.:0.0000  
    +##  Median :0.0000   Median :0.0000   Median :0.00000   Median :0.0000  
    +##  Mean   :0.1406   Mean   :0.1406   Mean   :0.04688   Mean   :0.2812  
    +##  3rd Qu.:0.0000   3rd Qu.:0.0000   3rd Qu.:0.00000   3rd Qu.:0.5000  
    +##  Max.   :1.0000   Max.   :1.0000   Max.   :0.25000   Max.   :1.0000  
    +##                                                                      
    +##  Hydrated Iron oxide Organic matter   Sulfate+Organic matter
    +##  Min.   :0.00000     Min.   :0.0000   Min.   :0.0000        
    +##  1st Qu.:0.00000     1st Qu.:0.0000   1st Qu.:0.0000        
    +##  Median :0.00000     Median :1.0000   Median :0.0000        
    +##  Mean   :0.01562     Mean   :0.5938   Mean   :0.2188        
    +##  3rd Qu.:0.00000     3rd Qu.:1.0000   3rd Qu.:0.2500        
    +##  Max.   :0.25000     Max.   :1.0000   Max.   :1.0000        
    +##                                                             
    +##  Other hydrated phases Phyllosilicates      Chlorite     
    +##  Min.   :0.0000        Min.   :0.00000   Min.   :0.0000  
    +##  1st Qu.:0.0000        1st Qu.:0.00000   1st Qu.:0.0000  
    +##  Median :0.2500        Median :0.00000   Median :0.0000  
    +##  Mean   :0.4375        Mean   :0.09375   Mean   :0.0625  
    +##  3rd Qu.:1.0000        3rd Qu.:0.06250   3rd Qu.:0.0000  
    +##  Max.   :1.0000        Max.   :0.50000   Max.   :0.5000  
    +##                                                          
    +##  Kaolinite (hydrous Al-clay)    Chromite        Ilmenite     Zircon/Baddeleyite
    +##  Min.   :0.0000              Min.   :0.000   Min.   :0.000   Min.   :0.000     
    +##  1st Qu.:0.0000              1st Qu.:0.000   1st Qu.:0.000   1st Qu.:0.000     
    +##  Median :0.0000              Median :0.000   Median :0.000   Median :0.000     
    +##  Mean   :0.1875              Mean   :0.125   Mean   :0.125   Mean   :0.125     
    +##  3rd Qu.:0.0000              3rd Qu.:0.000   3rd Qu.:0.000   3rd Qu.:0.000     
    +##  Max.   :1.0000              Max.   :1.000   Max.   :1.000   Max.   :1.000     
    +##                                                                                
    +##  Fe-Mg-clay minerals    Spinels           sample              name   
    +##  Min.   :0.0000      Min.   :0.0000   Min.   : 1.00   Atsah     : 1  
    +##  1st Qu.:0.0000      1st Qu.:0.0000   1st Qu.: 4.75   Bearwallow: 1  
    +##  Median :0.0000      Median :0.0000   Median : 8.50   Coulettes : 1  
    +##  Mean   :0.1875      Mean   :0.0625   Mean   : 8.50   Hahonih   : 1  
    +##  3rd Qu.:0.0000      3rd Qu.:0.0000   3rd Qu.:12.25   Hazeltop  : 1  
    +##  Max.   :1.0000      Max.   :0.5000   Max.   :16.00   Kukaklek  : 1  
    +##                                                       (Other)   :10  
    +##        SampleType         campaign         abrasion feldspar plagioclase
    +##  atmospheric: 1   Crater Floor:9   Alfalfa     :2   0:14     0:13       
    +##  regolith   : 0   Delta Front :7   Bellegarde  :2   1: 2     1: 3       
    +##  rock core  :15   Margin Unit :0   Berry Hollow:2                       
    +##                                    Dourbes     :2                       
    +##                                    Novarupta   :2                       
    +##                                    Quartier    :2                       
    +##                                    (Other)     :4                       
    +##  pyroxene olivine quartz apatite FeTi_Oxides Iron_Oxide Sulfate Perchlorates
    +##  0: 5     0: 6    0:14   0:13    0:13        0:9        0: 4    0:15        
    +##  1:11     1:10    1: 2   1: 3    1: 3        1:7        1:12    1: 1        
    +##                                                                             
    +##                                                                             
    +##                                                                             
    +##                                                                             
    +##                                                                             
    +##  Phosphate Ca_Sulfate Carbonate Fe_Mg_clay Fe_Mg_carbonate Mg_sulfate
    +##  0:11      0:10       0: 1      0:13       0:14            0:13      
    +##  1: 5      1: 6       1:15      1: 3       1: 2            1: 3      
    +##                                                                      
    +##                                                                      
    +##                                                                      
    +##                                                                      
    +##                                                                      
    +##  Phyllosilicates Chlorite Halite Organic_matter Hydrated_Ca_Sulfate
    +##  0:12            0:14     0:13   0: 5           0:14               
    +##  1: 4            1: 2     1: 3   1:11           1: 2               
    +##                                                                    
    +##                                                                    
    +##                                                                    
    +##                                                                    
    +##                                                                    
    +##  Hydrated_Sulfates Hydrated_Mg_Fe_Sulfate Na_Perchlorate Amorphous_Silicate
    +##  0:14              0:13                   0:15           0:9               
    +##  1: 2              1: 3                   1: 1           1:7               
    +##                                                                            
    +##                                                                            
    +##                                                                            
    +##                                                                            
    +##                                                                            
    +##  Hydrated_Carbonates Disordered_Silicates Hydrated_Iron_Oxide
    +##  0:16                0:14                 0:15               
    +##                      1: 2                 1: 1               
    +##                                                              
    +##                                                              
    +##                                                              
    +##                                                              
    +##                                                              
    +##  Sulfate+Organic_Matter Other_hydrated_phases Kaolinite Chromite Ilmenite
    +##  0:11                   0:8                   0:13      0:14     0:14    
    +##  1: 5                   1:8                   1: 3      1: 2     1: 2    
    +##                                                                          
    +##                                                                          
    +##                                                                          
    +##                                                                          
    +##                                                                          
    +##  Zircon/Baddeleyite Spinels
    +##  0:14               0:14   
    +##  1: 2               1: 2   
    +##                            
    +##                            
    +##                            
    +##                            
    +## 
    +
    str(sherloc_lithology.matrix)
    +
    ##  num [1:16, 1:70] 1 1 1 0 0 0 0 0 0 0 ...
    +##  - attr(*, "dimnames")=List of 2
    +##   ..$ : NULL
    +##   ..$ : chr [1:70] "Plagioclase" "Sulfate" "Ca-sulfate" "Hydrated Ca-sulfate" ...
    +
    1. Scale this data appropriately (you can choose the scaling method or decide to not scale data): Explain why you chose a scaling method or to not scale. (3 pts) Since the dataset contains both @@ -2938,17 +3098,15 @@

      4 Analysis of Data (Part best number of clusters. Indicate the number of points in each clusters. Coordinate with your team so you try different approaches. If you want to share results with your team mates, make sure to use the same random -seeds. (6 pts)

    2. -
    3. _Perform a creative analysis that provides -insights into what one or more of the clusters are and what they tell -you about the MARS data: Alternatively do another creative analysis of -your datasets that leads to one of more findings. Make sure to explain -what your analysis and discuss your the results.

    4. +seeds. (6 pts) After darwing the wss plot of the matrix, I use elbow +method plot to decide the best number of clusters. In this case, The +elbow appears to form around 3 or 4 clusters. The sharp drop in the WCSS +from 2 clusters to 3 clusters suggests that adding a third cluster +significantly improves the clustering quality. Therefore, I choose 3 +clusters. The first cluster has 7 points, the second cluster has 2 +points and the third cluster has 7 points.

    -
    sherloc_lithology.matrix[is.na(sherloc_lithology.matrix)] <- mean(sherloc_lithology.matrix, na.rm = TRUE)
    -scaled_data <- scale(sherloc_lithology.matrix)
    -
    dim(sherloc_lithology.df)
    -
    ## [1] 16 80
    +

    CLustering

    # A user-defined function to examine clusters and plot the results
     wssplot <- function(data, nc=15, seed=10){
       wss <- data.frame(cluster=1:nc, quality=c(0))
    @@ -2974,14 +3132,6 @@ 

    4 Analysis of Data (Part According to this heat map, the features at left have a high mean than the features at right. Moreover, cluster 2 has an over all more high mean than cluster 1 and cluster 3.

    -

    Now, performing PCA.

    -
    # Perform the PCA on the matrix we created earlier
    -
    -sherloc_lithology.pca <- prcomp(sherloc_lithology.matrix, scale=FALSE)
    -
    -# generate the Scree plot
    -ggscreeplot(sherloc_lithology.pca)
    -

    Next, indicating how many samples are in each cluster

    library(knitr)
     # clusters sizes are in the km object produced by kmeans
    @@ -3010,6 +3160,21 @@ 

    4 Analysis of Data (Part +
      +
    1. _Perform a creative analysis that provides insights +into what one or more of the clusters are and what they tell you about +the MARS data: Alternatively do another creative analysis of your +datasets that leads to one of more findings. Make sure to explain what +your analysis and discuss your the results.
      +Now, performing PCA.
    2. +
    +
    # Perform the PCA on the matrix we created earlier
    +
    +sherloc_lithology.pca <- prcomp(sherloc_lithology.matrix, scale=FALSE)
    +
    +# generate the Scree plot
    +ggscreeplot(sherloc_lithology.pca)
    +

    Creative analysis:

    summary(sherloc_lithology.pca)
    ## Importance of components:
    @@ -3038,105 +3203,128 @@ 

    4 Analysis of Data (Part principal components should be considered for further analysis, as they explain the majority of the variance in the dataset. After the 4th component, the additional variance explained becomes minimal.

    -
    loadings <- sherloc_lithology.pca$rotation[,1:4]
    +
    loadings <- abs(sherloc_lithology.pca$rotation[, 1:3])
     print(loadings)
    -
    ##                                      PC1          PC2          PC3          PC4
    -## Plagioclase                 -0.064336916  0.253285711  0.034736225  0.011964995
    -## Sulfate                     -0.175146396  0.057235074 -0.031239837  0.302918236
    -## Ca-sulfate                  -0.232159520  0.167134575 -0.064154734 -0.021631913
    -## Hydrated Ca-sulfate         -0.042131612  0.170024387  0.021970393  0.023568451
    -## Mg-sulfate                  -0.200670557 -0.107436782 -0.114769312 -0.033532288
    -## Hydrated Sulfates            0.046640374 -0.046533930  0.004709232  0.211811697
    -## Hydrated Mg-Fe sulfate      -0.200670557 -0.107436782 -0.114769312 -0.033532288
    -## Perchlorates                -0.022205304  0.083261324  0.012765831 -0.011603456
    -## Na-perchlorate              -0.011102652  0.041630662  0.006382916 -0.005801728
    -## Amorphous Silicate           0.017782440  0.039123645  0.003335076  0.124303014
    -## Phosphate                   -0.050067834  0.156937069  0.139435041 -0.027420114
    -## Pyroxene                     0.205440349  0.175242080 -0.113777068  0.129707690
    -## Olivine                      0.199073864 -0.131670868  0.156241523  0.150758082
    -## Carbonate                    0.128752482  0.006768303  0.124116776  0.122879865
    -## Fe-Mg carbonate              0.090812262  0.012522980 -0.038558702 -0.058532299
    -## Hydrated Carbonates          0.000000000  0.000000000  0.000000000  0.000000000
    -## Disordered Silicates         0.087911478 -0.018904080 -0.101611247 -0.172254385
    -## Feldspar                     0.087911478 -0.018904080 -0.101611247 -0.172254385
    -## Quartz                       0.021977870 -0.004726020 -0.025402812 -0.043063596
    -## Apatite                     -0.010321118 -0.046989967  0.231737838 -0.099076266
    -## FeTi oxides                 -0.047682938  0.190839718  0.025161851  0.020667587
    -## Halite                       0.017151739  0.023946076 -0.006448218 -0.017533939
    -## Iron oxide                   0.002321888  0.246964416 -0.025709074 -0.088795272
    -## Hydrated Iron oxide         -0.005551326  0.020815331  0.003191458 -0.002900864
    -## Organic matter              -0.022898001 -0.214954717 -0.167587308  0.118698855
    -## Sulfate+Organic matter      -0.020247980 -0.106056547  0.030089121  0.187897087
    -## Other hydrated phases        0.225821526 -0.068591591 -0.097707669  0.203869887
    -## Phyllosilicates              0.066658805 -0.006321295 -0.060445299 -0.100760267
    -## Chlorite                     0.043955739 -0.009452040 -0.050805623 -0.086127193
    -## Kaolinite (hydrous Al-clay) -0.200670557 -0.107436782 -0.114769312 -0.033532288
    -## Chromite                    -0.004769792 -0.067805298  0.228546380 -0.096175402
    -## Ilmenite                    -0.004769792 -0.067805298  0.228546380 -0.096175402
    -## Zircon/Baddeleyite          -0.004769792 -0.067805298  0.228546380 -0.096175402
    -## Fe-Mg-clay minerals         -0.200670557 -0.107436782 -0.114769312 -0.033532288
    -## Spinels                     -0.002384896 -0.033902649  0.114273190 -0.048087701
    -## feldspar                     0.087911478 -0.018904080 -0.101611247 -0.172254385
    -## plagioclase                 -0.064336916  0.253285711  0.034736225  0.011964995
    -## pyroxene                     0.205440349  0.175242080 -0.113777068  0.129707690
    -## olivine                      0.265007473 -0.145848928  0.080033088  0.021567293
    -## quartz                       0.087911478 -0.018904080 -0.101611247 -0.172254385
    -## apatite                     -0.026975096  0.015456026  0.241312212 -0.107778858
    -## FeTi_Oxides                 -0.064336916  0.253285711  0.034736225  0.011964995
    -## Iron_Oxide                   0.114386824  0.246904610 -0.105433723 -0.218821689
    -## Sulfate                     -0.178723740  0.006381100  0.140169948  0.230786684
    -## Perchlorates                -0.022205304  0.083261324  0.012765831 -0.011603456
    -## Phosphate                   -0.069106708  0.185480413  0.263282605 -0.084210407
    -## Ca_Sulfate                  -0.265007473  0.145848928 -0.080033088 -0.021567293
    -## Carbonate                    0.022205304 -0.083261324 -0.012765831  0.011603456
    -## Fe_Mg_clay                  -0.200670557 -0.107436782 -0.114769312 -0.033532288
    -## Fe_Mg_carbonate              0.090812262  0.012522980 -0.038558702 -0.058532299
    -## Mg_sulfate                  -0.200670557 -0.107436782 -0.114769312 -0.033532288
    -## Phyllosilicates              0.178723740 -0.006381100 -0.140169948 -0.230786684
    -## Chlorite                     0.087911478 -0.018904080 -0.101611247 -0.172254385
    -## Halite                       0.068606958  0.095784304 -0.025792870 -0.070135755
    -## Organic_matter              -0.026475345 -0.265808691  0.003822477  0.046567303
    -## Hydrated_Ca_Sulfate         -0.042131612  0.170024387  0.021970393  0.023568451
    -## Hydrated_Sulfates            0.046640374 -0.046533930  0.004709232  0.211811697
    -## Hydrated_Mg_Fe_Sulfate      -0.200670557 -0.107436782 -0.114769312 -0.033532288
    -## Na_Perchlorate              -0.022205304  0.083261324  0.012765831 -0.011603456
    -## Amorphous_Silicate           0.026716609  0.181623180  0.026392880  0.360494374
    -## Hydrated_Carbonates          0.000000000  0.000000000  0.000000000  0.000000000
    -## Disordered_Silicates         0.087911478 -0.018904080 -0.101611247 -0.172254385
    -## Hydrated_Iron_Oxide         -0.022205304  0.083261324  0.012765831 -0.011603456
    -## Sulfate+Organic_Matter      -0.023825324 -0.156910520  0.201498906  0.115765536
    -## Other_hydrated_phases        0.269777265 -0.078043631 -0.148513293  0.117742695
    -## Kaolinite                   -0.200670557 -0.107436782 -0.114769312 -0.033532288
    -## Chromite                    -0.004769792 -0.067805298  0.228546380 -0.096175402
    -## Ilmenite                    -0.004769792 -0.067805298  0.228546380 -0.096175402
    -## Zircon/Baddeleyite          -0.004769792 -0.067805298  0.228546380 -0.096175402
    -## Spinels                     -0.004769792 -0.067805298  0.228546380 -0.096175402
    -

    Based on the result, SHERLOC measurements dominate PC1 and lithology +

    ##                                     PC1         PC2         PC3
    +## Plagioclase                 0.064336916 0.253285711 0.034736225
    +## Sulfate                     0.175146396 0.057235074 0.031239837
    +## Ca-sulfate                  0.232159520 0.167134575 0.064154734
    +## Hydrated Ca-sulfate         0.042131612 0.170024387 0.021970393
    +## Mg-sulfate                  0.200670557 0.107436782 0.114769312
    +## Hydrated Sulfates           0.046640374 0.046533930 0.004709232
    +## Hydrated Mg-Fe sulfate      0.200670557 0.107436782 0.114769312
    +## Perchlorates                0.022205304 0.083261324 0.012765831
    +## Na-perchlorate              0.011102652 0.041630662 0.006382916
    +## Amorphous Silicate          0.017782440 0.039123645 0.003335076
    +## Phosphate                   0.050067834 0.156937069 0.139435041
    +## Pyroxene                    0.205440349 0.175242080 0.113777068
    +## Olivine                     0.199073864 0.131670868 0.156241523
    +## Carbonate                   0.128752482 0.006768303 0.124116776
    +## Fe-Mg carbonate             0.090812262 0.012522980 0.038558702
    +## Hydrated Carbonates         0.000000000 0.000000000 0.000000000
    +## Disordered Silicates        0.087911478 0.018904080 0.101611247
    +## Feldspar                    0.087911478 0.018904080 0.101611247
    +## Quartz                      0.021977870 0.004726020 0.025402812
    +## Apatite                     0.010321118 0.046989967 0.231737838
    +## FeTi oxides                 0.047682938 0.190839718 0.025161851
    +## Halite                      0.017151739 0.023946076 0.006448218
    +## Iron oxide                  0.002321888 0.246964416 0.025709074
    +## Hydrated Iron oxide         0.005551326 0.020815331 0.003191458
    +## Organic matter              0.022898001 0.214954717 0.167587308
    +## Sulfate+Organic matter      0.020247980 0.106056547 0.030089121
    +## Other hydrated phases       0.225821526 0.068591591 0.097707669
    +## Phyllosilicates             0.066658805 0.006321295 0.060445299
    +## Chlorite                    0.043955739 0.009452040 0.050805623
    +## Kaolinite (hydrous Al-clay) 0.200670557 0.107436782 0.114769312
    +## Chromite                    0.004769792 0.067805298 0.228546380
    +## Ilmenite                    0.004769792 0.067805298 0.228546380
    +## Zircon/Baddeleyite          0.004769792 0.067805298 0.228546380
    +## Fe-Mg-clay minerals         0.200670557 0.107436782 0.114769312
    +## Spinels                     0.002384896 0.033902649 0.114273190
    +## feldspar                    0.087911478 0.018904080 0.101611247
    +## plagioclase                 0.064336916 0.253285711 0.034736225
    +## pyroxene                    0.205440349 0.175242080 0.113777068
    +## olivine                     0.265007473 0.145848928 0.080033088
    +## quartz                      0.087911478 0.018904080 0.101611247
    +## apatite                     0.026975096 0.015456026 0.241312212
    +## FeTi_Oxides                 0.064336916 0.253285711 0.034736225
    +## Iron_Oxide                  0.114386824 0.246904610 0.105433723
    +## Sulfate                     0.178723740 0.006381100 0.140169948
    +## Perchlorates                0.022205304 0.083261324 0.012765831
    +## Phosphate                   0.069106708 0.185480413 0.263282605
    +## Ca_Sulfate                  0.265007473 0.145848928 0.080033088
    +## Carbonate                   0.022205304 0.083261324 0.012765831
    +## Fe_Mg_clay                  0.200670557 0.107436782 0.114769312
    +## Fe_Mg_carbonate             0.090812262 0.012522980 0.038558702
    +## Mg_sulfate                  0.200670557 0.107436782 0.114769312
    +## Phyllosilicates             0.178723740 0.006381100 0.140169948
    +## Chlorite                    0.087911478 0.018904080 0.101611247
    +## Halite                      0.068606958 0.095784304 0.025792870
    +## Organic_matter              0.026475345 0.265808691 0.003822477
    +## Hydrated_Ca_Sulfate         0.042131612 0.170024387 0.021970393
    +## Hydrated_Sulfates           0.046640374 0.046533930 0.004709232
    +## Hydrated_Mg_Fe_Sulfate      0.200670557 0.107436782 0.114769312
    +## Na_Perchlorate              0.022205304 0.083261324 0.012765831
    +## Amorphous_Silicate          0.026716609 0.181623180 0.026392880
    +## Hydrated_Carbonates         0.000000000 0.000000000 0.000000000
    +## Disordered_Silicates        0.087911478 0.018904080 0.101611247
    +## Hydrated_Iron_Oxide         0.022205304 0.083261324 0.012765831
    +## Sulfate+Organic_Matter      0.023825324 0.156910520 0.201498906
    +## Other_hydrated_phases       0.269777265 0.078043631 0.148513293
    +## Kaolinite                   0.200670557 0.107436782 0.114769312
    +## Chromite                    0.004769792 0.067805298 0.228546380
    +## Ilmenite                    0.004769792 0.067805298 0.228546380
    +## Zircon/Baddeleyite          0.004769792 0.067805298 0.228546380
    +## Spinels                     0.004769792 0.067805298 0.228546380
    +
    threshold <- 0.2
    +important_vars <- apply(loadings, 1, function(x) any(x > threshold))
    +sherloc_lithology_filtered <- sherloc_lithology.pca
    +sherloc_lithology_filtered$rotation <- sherloc_lithology_filtered$rotation[important_vars, ]
    +

    Using loading to show how much each variable contributes to the +principal components. Then, I filtered the variables which only keep the +variables that has a contribution greater than 0.2. The high positive or +negative values in the loading are most important to each component +Based on the result, SHERLOC measurements dominate PC1 and lithology measurements dominate PC2, we could infer that PC1 captures the primary chemical or spectroscopic composition of the Martian surface, while PC2 relates to the geological context.

    Create a PCA biplot to visualize the clusters

    # For this lab we'll create a PCA biplot the easy way using ggbiplot!
    -ggbiplot::ggbiplot(sherloc_lithology.pca,
    -                   choices = c(1,2),
    +ggbiplot::ggbiplot(sherloc_lithology_filtered,
    +                   choices = c(1, 2),
                        labels = sherloc_lithology.df$type,
                        groups = as.factor(km$cluster)) +
    -  xlim(-2,2) + ylim(-2,2) 
    -
    ## Warning: Removed 2 rows containing missing values or values outside the scale range
    -## (`geom_text()`).
    -

    + xlim(-2, 2) + ylim(-2, 2) + + ggtitle("Filtered Biplot: PC1 vs PC2")
    +

    +Iron Oxide, Amorphous Silicate, Pyroxene, Olivine, Hydrated Sulfates: +These variables contribute the most to PC1, suggesting that PC1 +continues to represent a contrast between igneous materials (e.g., +pyroxene, olivine) and sedimentary or hydrated minerals (e.g., hydrated +sulfates). Moreover, as these variables group closely together, which +indicates a common geological origin. This likely corresponds to igneous +regions on Mars Phyllosilicates and Iron Oxide: These variables are also +significant contributors to PC2, meaning PC2 is likely to represent +variations within sedimentary environments which separate different +types of hydrated minerals and phyllosilicates. This could reflect +differences in the extent or type of chemical alteration due to +water.

    make another PCA biplot to create a comparison between PC1 and PC3

    -
    ggbiplot::ggbiplot(sherloc_lithology.pca,
    -                   choices = c(1,3),
    +
    ggbiplot::ggbiplot(sherloc_lithology_filtered,
    +                   choices = c(1, 3),
                        labels = sherloc_lithology.df$type,
                        groups = as.factor(km$cluster)) +
    -  xlim(-2,2) + ylim(-2,2) 
    + xlim(-2, 2) + ylim(-2, 2) + + ggtitle("Filtered Biplot: PC1 vs PC3")
    ## Warning: Removed 2 rows containing missing values or values outside the scale range
    -## (`geom_text()`).
    -## Removed 2 rows containing missing values or values outside the scale range
     ## (`geom_text()`).
    -

    +

    +Organic Matter and Phosphate: These variables are much more important in +PC3 than PC2, suggesting that PC3 may capture some trend related to the +presence of organic compounds or chemical processes that differ from +those driving the first two PCs, distinguishing areas where organic +compounds or specific chemical interactions are more prevalent.

    5 Preparation of Team diff --git a/StudentNotebooks/Assignment02/zhaot4-f24-assignment2.pdf b/StudentNotebooks/Assignment02/zhaot4-f24-assignment2.pdf index 7e0af2aead9852565a2b3b5c9b1605c989d5c13c..64464fc7dc56e368a259194e812d9737637111f4 100644 GIT binary patch delta 92479 zcmZU)Q*>@?)3qDhwr$(CZQGjh6Wew&V>_9dv2EM7jeo86ekZ%_vpN~o+I>)0^mX829mUI^Ef35Y z$!p<`EJy;-F9!Dba)haGzZ`pf$A2;a+E@MfMH&CL z6#to@9a>R9S~h>8>TUK*IYJWul|&YV%W74FvuLDLpzCc|zm5^{n=hfaOE9U33$;5$ zqEuvf&8n48$UB2dD<4GL?5v!n=ps0NXS`^kD#8R%K%4VOZhx*Uz@0nMT=&40C}I&6 zDi_5~ov!&dJ_{r!ll#!Aog(h#`ja$_X;~+j`{OGD+LfhxGOz*2XLMIRVpUDP%^dpO z#r-wx<_@1lJHB=k+Hv&a?ym{uvxskdXC31-D@f60>qm?(2Z>#)(Of0@CRXh}L~!*0 zo4OK;POab+Pp)&YT1~w%OjzA*Se9?mG+;q-rua2#`{$h(_yAx}8sZ69+#<$A^*59cj+^@7eYi8pW7PDvKF6fW z0py*yi=rN}x5V=*yQPWvDo(7T_xv1vepYczVyM&RXpk@ppuJNtT87q6!BXhkMcHmO z51{f_e55pec!7(05F#FH3xt<7;EXAiGa;<*su49NqZ5BcS;96(Dzr2x0qu?+(# zFj)m+QXh%tk;J)+c=*6OuC-l=#Bpv_y=yEFh@LR&rK#(fy(7D3bx*UTG?8pnW-`#> 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bytes 3 files changed, 13 insertions(+), 7 deletions(-) diff --git a/StudentNotebooks/Assignment02/zhaot4-f24-assignment2.Rmd b/StudentNotebooks/Assignment02/zhaot4-f24-assignment2.Rmd index 406fb80..6954e4a 100644 --- a/StudentNotebooks/Assignment02/zhaot4-f24-assignment2.Rmd +++ b/StudentNotebooks/Assignment02/zhaot4-f24-assignment2.Rmd @@ -474,11 +474,14 @@ Based on the result, SHERLOC measurements dominate PC1 and lithology measurement Create a PCA biplot to visualize the clusters ```{r} +sherloc_lithology.df$cluster <- factor(km$cluster, + levels = c(1, 2, 3), + labels = c("Cluster 1", "Cluster 2", "Cluster 3")) # For this lab we'll create a PCA biplot the easy way using ggbiplot! ggbiplot::ggbiplot(sherloc_lithology_filtered, choices = c(1, 2), labels = sherloc_lithology.df$type, - groups = as.factor(km$cluster)) + + groups = sherloc_lithology.df$cluster) + xlim(-2, 2) + ylim(-2, 2) + ggtitle("Filtered Biplot: PC1 vs PC2") ``` @@ -491,7 +494,7 @@ make another PCA biplot to create a comparison between PC1 and PC3 ggbiplot::ggbiplot(sherloc_lithology_filtered, choices = c(1, 3), labels = sherloc_lithology.df$type, - groups = as.factor(km$cluster)) + + groups = sherloc_lithology.df$cluster) + xlim(-2, 2) + ylim(-2, 2) + ggtitle("Filtered Biplot: PC1 vs PC3") diff --git a/StudentNotebooks/Assignment02/zhaot4-f24-assignment2.html b/StudentNotebooks/Assignment02/zhaot4-f24-assignment2.html index 88ef6c7..8c5abfa 100644 --- a/StudentNotebooks/Assignment02/zhaot4-f24-assignment2.html +++ b/StudentNotebooks/Assignment02/zhaot4-f24-assignment2.html @@ -3289,14 +3289,17 @@

    4 Analysis of Data (Part chemical or spectroscopic composition of the Martian surface, while PC2 relates to the geological context.

    Create a PCA biplot to visualize the clusters

    -
    # For this lab we'll create a PCA biplot the easy way using ggbiplot!
    +
    sherloc_lithology.df$cluster <- factor(km$cluster, 
    +                                       levels = c(1, 2, 3), 
    +                                       labels = c("Cluster 1", "Cluster 2", "Cluster 3"))
    +# For this lab we'll create a PCA biplot the easy way using ggbiplot!
     ggbiplot::ggbiplot(sherloc_lithology_filtered,
                        choices = c(1, 2),
                        labels = sherloc_lithology.df$type,
    -                   groups = as.factor(km$cluster)) +
    +                   groups = sherloc_lithology.df$cluster) +
       xlim(-2, 2) + ylim(-2, 2) +
       ggtitle("Filtered Biplot: PC1 vs PC2") 
    -

    +

    Iron Oxide, Amorphous Silicate, Pyroxene, Olivine, Hydrated Sulfates: These variables contribute the most to PC1, suggesting that PC1 continues to represent a contrast between igneous materials (e.g., @@ -3314,12 +3317,12 @@

    4 Analysis of Data (Part
    ggbiplot::ggbiplot(sherloc_lithology_filtered,
                        choices = c(1, 3),
                        labels = sherloc_lithology.df$type,
    -                   groups = as.factor(km$cluster)) +
    +                   groups = sherloc_lithology.df$cluster) +
       xlim(-2, 2) + ylim(-2, 2) +
       ggtitle("Filtered Biplot: PC1 vs PC3") 
    ## Warning: Removed 2 rows containing missing values or values outside the scale range
     ## (`geom_text()`).
    -

    +

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++++++---- .../Assignment02/zhaot4-f24-assignment2.pdf | Bin 337328 -> 337360 bytes 3 files changed, 7 insertions(+), 5 deletions(-) diff --git a/StudentNotebooks/Assignment02/zhaot4-f24-assignment2.Rmd b/StudentNotebooks/Assignment02/zhaot4-f24-assignment2.Rmd index 6954e4a..000c244 100644 --- a/StudentNotebooks/Assignment02/zhaot4-f24-assignment2.Rmd +++ b/StudentNotebooks/Assignment02/zhaot4-f24-assignment2.Rmd @@ -386,7 +386,7 @@ Each team has been assigned one of six datasets: **For the data set assigned to your team, perform the following steps.** Feel free to use the methods/code from Assignment 1 as desired. Communicate with your teammates. Make sure that you are doing different variations of below analysis so that no team member does the exact same analysis. If you want to use the same clustering for your team (which is okay but then vary rest), make sure you use the same random seeds. 1. _Describe the data set contained in the data frame and matrix:_ How many rows does it have and how many features? Which features are measurements and which features are metadata about the samples? (3 pts) -There is 16 rows and 70 features. min, max, mean, median, 1st qu, 3rd qu are measurements, and +There is 16 rows and 99 features. measurements are comprised with all chemical compound such as sulfate, Ca-sulfate and Hydrated Ca-sulfate, and metadata about the samples are as the following: sample, name, type, campaign, abrasion. ```{r} summary(sherloc_lithology.df) diff --git a/StudentNotebooks/Assignment02/zhaot4-f24-assignment2.html b/StudentNotebooks/Assignment02/zhaot4-f24-assignment2.html index 8c5abfa..eb91436 100644 --- a/StudentNotebooks/Assignment02/zhaot4-f24-assignment2.html +++ b/StudentNotebooks/Assignment02/zhaot4-f24-assignment2.html @@ -11,7 +11,7 @@ - + Mars 2020 Mission Data Notebook-zhaot4: @@ -1625,7 +1625,7 @@

    Mars 2020 Mission Data Notebook-zhaot4:

    Mars DAR Assignment 2 (Fall 2024)

    Tianhao Zhao

    -

    09 September 2024

    +

    10 September 2024

    @@ -2925,8 +2925,10 @@

    4 Analysis of Data (Part
  • Describe the data set contained in the data frame and matrix: How many rows does it have and how many features? Which features are measurements and which features are metadata about the -samples? (3 pts) There is 16 rows and 70 features. min, max, mean, -median, 1st qu, 3rd qu are measurements, and
  • +samples? (3 pts) There is 16 rows and 99 features. measurements are +comprised with all chemical compound such as sulfate, Ca-sulfate and +Hydrated Ca-sulfate, and metadata about the samples are as the +following: sample, name, type, campaign, abrasion.
    summary(sherloc_lithology.df)
    ##      sample               type           campaign         abrasion
    diff --git a/StudentNotebooks/Assignment02/zhaot4-f24-assignment2.pdf b/StudentNotebooks/Assignment02/zhaot4-f24-assignment2.pdf
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