From 3c1e2d2dd3a77529751c7a23d0c835a5247ce94c Mon Sep 17 00:00:00 2001 From: lahira Date: Wed, 6 Nov 2024 12:47:25 -0500 Subject: [PATCH] Finished Notebook 5 --- .../Assignment05/lahira-assignment05.Rmd | 775 ++++++++++ .../Assignment05/lahira-assignment05.html | 1362 +++++++++++++++++ .../Assignment05/lahira-assignment05.pdf | Bin 0 -> 1056112 bytes 3 files changed, 2137 insertions(+) create mode 100644 StudentNotebooks/Assignment05/lahira-assignment05.Rmd create mode 100644 StudentNotebooks/Assignment05/lahira-assignment05.html create mode 100644 StudentNotebooks/Assignment05/lahira-assignment05.pdf diff --git a/StudentNotebooks/Assignment05/lahira-assignment05.Rmd b/StudentNotebooks/Assignment05/lahira-assignment05.Rmd new file mode 100644 index 0000000..57b08aa --- /dev/null +++ b/StudentNotebooks/Assignment05/lahira-assignment05.Rmd @@ -0,0 +1,775 @@ +--- +title: "DAR F24 Notebook 5" +author: "Aadi Lahiri" +date: "`r Sys.Date()`" +output: + pdf_document: + toc: yes + html_document: + toc: yes +subtitle: "Mars" +--- + +## Weekly Work Summary + +* RCS ID: Lahira +* Project Name: Mars +* Summary of work since last week + + * Log scaled LIBS data set and performed PCA + * Did some research on LIBS + * Scale LIBS on Earth reference quartiles + * Compare old plots with LIBS with earth reference samples removed + +* NEW: Summary of github issues added and worked + + * Worked on Log Scaling the LIBS dataset + * Worked on Earth references for LIBS + * Worked on Scaling LIBS on Earth References + * Worked on Slides for Dr. Rogers + +* Summary of github commits + + * branch is dar-lahira + * Pulled this notebook (lahira-assignment05.rmd) + +* List of presentations, papers, or other outputs + + * https://www.mdpi.com/1996-1944/16/20/6641 + +* List of references (if necessary) +* Indicate any use of group shared code base +* Indicate which parts of your described work were done by you or as part of joint efforts + +## Personal Contribution + +* This entire Notebook from Questions 3-6 were done by me since the last notebook was due. + +```{r setup, include=FALSE} +knitr::opts_chunk$set(echo = TRUE) + +# Set the default CRAN repository +local({r <- getOption("repos") + r["CRAN"] <- "http://cran.r-project.org" + options(repos=r) +}) + +if (!require("pandoc")) { + install.packages("pandoc") + library(pandoc) +} + +# Required packages for M20 LIBS analysis +if (!require("rmarkdown")) { + install.packages("rmarkdown") + library(rmarkdown) +} +if (!require("tidyverse")) { + install.packages("tidyverse") + library(tidyverse) +} +if (!require("stringr")) { + install.packages("stringr") + library(stringr) +} + +if (!require("ggbiplot")) { + install.packages("ggbiplot") + library(ggbiplot) +} + +if (!require("pheatmap")) { + install.packages("pheatmap") + library(pheatmap) +} + +if (!require("caret")) { + install.packages("caret") + library(caret) +} + +if (!require("ggplot2")) { + install.packages("ggbiplot") + library(ggbiplot) +} + +if (!require("knitr")) { + install.packages("knitr") + library(knitr) +} + +if (!require("BBmisc")) { + install.packages("BBmisc") + library(BBmisc) +} + +if (!require("ggtern")) { + install.packages("ggtern") + library(ggtern) +} +``` + +## Analysis: Question 1: Exploring LIBS data + +### Question being asked + +I want to figure out what the cation compositions of the samples can tell us about the LIBS data, and how aggregating the data can change this picture. I also want to plot the PIXL data onto the LIBS data to give the PIXL data some context. + +### Data Preparation + +Before I prepared the data, I wanted to learn more about LIBS in the first place to better understand how to use our data. LIBS stands for Laser-Induced breakdown Spectroscopy, which uses lasers to heat the surface of sample, and then reads the emitted wavelengths to determine the concentrations of various elements. However, the laser in LIBS is not very consistent, so it takes the average of the multiple firings, which is why there is a standard deviation for each measurement. + +To start the analysis, I loaded the PIXL and LIBS data frames, and then took the sums of three specific elemental combinations: Silicon and Aluminium, Iron and Magnesium, and Calcium, Sodium, and Potassium. We can try to classify the LIBS samples based on the ratio of these 3 elements. + +```{r, result01_data} +# PIXL data added +pixl.df <- readRDS("/academics/MATP-4910-F24/DAR-Mars-F24/Data/samples_pixl_wide.Rds") +pixl.df[sapply(pixl.df, is.character)] <- lapply(pixl.df[sapply(pixl.df, is.character)], + as.factor) +pixl.df <- pixl.df[2:16,] #Excluding first, atmospheric sample + +#PIXL data, with identically reflected compositions +new_pixl_trim <- pixl.df %>% + dplyr::select(c("Na20","Mgo","Al203","Si02", "K20","Cao","FeO-T", campaign, type)) %>% + rename("Na2O"="Na20","MgO"="Mgo","Al2O3"="Al203","SiO2"="Si02","K2O"="K20", + "CaO"="Cao","FeOT"="FeO-T") +#take the sums of the specific elements, and rename type column +pixl_ternary <- new_pixl_trim %>% + mutate(x=(SiO2+Al2O3)/100,y=(FeOT+MgO)/100,z=(CaO+Na2O+K2O)/100, PIXL_Rock_Type = type) %>% + select(-c(SiO2,Al2O3,FeOT,MgO,CaO,Na2O,K2O)) %>% + drop_na() + +#This is for the labels on the Ternary Plot below +pixl_ternary <- cbind(pixl_ternary, Sample_display= + c("2","3","4,6,7","5,8,9","","","","", + "10,11","","12,13","","14,15","","16")) + +# Load the saved LIBS data with locations added +libs.df <- readRDS("/academics/MATP-4910-F24/DAR-Mars-F24/Data/supercam_libs_moc_loc.Rds") + +libs.df$point <- as.numeric(libs.df$point) + +#suppressing warnings here because target and point do not get a mean calculated, +#but thats is fine as we have the target anyways and point is no longer relevant +suppressWarnings( + libs.uniquetar <- + aggregate(libs.df, list(Target = libs.df$target), mean)) + +#drop target and point from the data frame +libs.uniquetar <- libs.uniquetar %>% select(!c(target,point)) + +#Sum the elements we are looking at +libs.df <- libs.df %>% + mutate(y = (FeOT + MgO) / 100, z = (CaO+Na2O+K2O) / 100, x = (SiO2 + Al2O3) / 100) + +#Same thing but aggregate +libs.uniquetar <- libs.uniquetar %>% + mutate(y = (FeOT + MgO) / 100, z = (CaO+Na2O+K2O) / 100, x = (SiO2 + Al2O3) / 100) +``` + +### Analysis: Methods and results + +I want to create a ternary plot of both the untouched LIBS data, and a ternary plot of the aggregate data to see if there are any differences. A ternary plot just is a graph of the relative compositions of 3 variables. By plotting the LIBS points, and clustering using kmeans, we can try to group similar samples together to see if they are all the same or similar rock type. I then plot the PIXL samples onto the same graph, and then classifying them by either Crater Floor or Delta Front to help classify those samples. The code for the PIXL data comes from Nicolas Morawski's Assignment 3 notebook. + +```{r, result01_analysis} +#Only select the columns we are going to use +libs_ternplot <- libs.df %>% select(c(x,y,z)) +libs_ternplot2 <- libs.uniquetar %>% select(c(x,y,z)) + +set.seed(1234) + +#kmeans on the original data +tern.km <- kmeans(libs_ternplot, centers=4) + +libs_ternplot <- cbind(libs_ternplot, LIBS_Cluster=as.factor(tern.km$cluster)) + +#ternary plot for LIBS data +ggtern(libs_ternplot, ggtern::aes(x=x, y=y, z=z, cluster=LIBS_Cluster)) + + #color by cluster + geom_point(aes(color=LIBS_Cluster), alpha = 0.5) + + theme_rgbw() + + labs(title="Mars 2020 LIBS Ternary Plot with PIXL Data", + subtitle="LIBS data Clustered by Cation Group with PIXL samples by Rock Type", + x="Si+Al2", + y="Fe+Mg", + z="Ca+Na2+K2") + + #suppress warnings here because of some warning with aes() + #add PIXL samples - atmospheric onto the ternary plot + suppressWarnings(geom_point( + data=pixl_ternary, ggtern::aes(x=x, y=y, z=z, + cluster=PIXL_Rock_Type, shape=PIXL_Rock_Type), + size = 2)) + + #Add labels to PIXL data corresponding to sample number + suppressWarnings(geom_text(data=pixl_ternary, + ggtern::aes(x=x, y=y, z=z, label=Sample_display, cluster=PIXL_Rock_Type, + hjust = ifelse(x > 0.43, 1, -0.1), # Horizontal adjust to avoid overlap + vjust = ifelse(x == 0.3668, 1.3, + ifelse(x == 0.375, 1, ifelse(x > 0.43, 1.5, -0.3))), + fontface="bold"), + size=2.7)) + +#kmeans on the aggregate data +tern.km2 <- kmeans(as.matrix(libs_ternplot2), centers=4) + +libs_ternplot2 <- cbind(libs_ternplot2, LIBS_Cluster=as.factor(tern.km2$cluster)) + +#plot for aggregate data +ggtern(libs_ternplot2, ggtern::aes(x=x, y=y, z=z,cluster=LIBS_Cluster)) + + geom_point(aes(color=LIBS_Cluster), alpha = 0.5) + + theme_rgbw() + + labs(title="Mars 2020 LIBS Ternary Plot Aggregated by Target with PIXL Data", + subtitle="LIBS data Clustered by Cation Group with PIXL samples by Rock Type", + x="Si+Al2", + y="Fe+Mg", + z="Ca+Na2+K2") + + suppressWarnings(geom_point( + data=pixl_ternary, ggtern::aes(x=x, y=y, z=z, + cluster=PIXL_Rock_Type, shape=PIXL_Rock_Type), + size = 2.5)) + + suppressWarnings(geom_text(data=pixl_ternary, + ggtern::aes(x=x, y=y, z=z, label=Sample_display, cluster=PIXL_Rock_Type, + hjust = ifelse(x > 0.43, 1, -0.1), # Horizontal adjust to avoid overlap + vjust = ifelse(x == 0.3668, 1.3, + ifelse(x == 0.375, 1, ifelse(x > 0.43, 1.5, -0.3))), + fontface="bold"), + size=2.7)) +``` + +### Discussion of results + +I created two ternary plots, one using the original LIBS dataset, and the other aggregated by target. Target I believe is the location from where the sample took place, so I wanted to see if eliminating the noise from multiple readings could help us identify trends in the data. For the ternary diagram itself, I chose the element groups from NASA's report on PIXL data for its different samples. From the ternary diagram, we see that most of the samples are high in both Fe+Mg and Al2, and low in Ca+Na2+K2. The samples that have higher Ca+Na2+K2 tend to have lower Fe+Mg and much lower Al2. From the clustering we see that cluster one tends to have high concentration of Si+Al2 and Fe+Mg, and very low concentrations of Ca+Na2+K2. Cluster 2 is mostly Fe+Mg, with a little Si+Al2. Cluster 3 is very diverse, but tends to be the samples with higher concentrations of Ca+Na2. Cluster 4 has higher concentrations of Si+Al2, wth lesser concentrations of Fe+Mg. + +When we look at the plot for the aggregate data, we see little difference in the key clusters of our graph. When ran with multiple seeds the clustering can group the points in the bottom right of the graph to different clusters, but I believe the one where they are their own cluster is the most accurate. + +Looking at the PIXL data, we see that sedimentary samples tend to be higher in Fe and Mg and lower in Si and Al, and are associated mostly with clusters 2 and 3. The igneous samples are the opposite, and appear in all clusters 1-3. + +## Analysis: Question 2: Further Classifying LIBS + +### Question being asked + +After making a Ternary plot, I still wanted to find out more about the LIBS samples. I want to make a TAS (Total Alkali Silica) plot, and use the igneous rock classification diagram to help us identify rocks from the LIBS samples. + +### Data Preparation + +I am going to compare the sum of the alkali elements to the sum of silica in each libs sample. + +I load the LIBS data and select only the columns I want. I also make the aggregate data again, and select the columns I want from that data as well. I also add a column, y= Na2O + K2O, which should be the total alkali content of the LIBS samples. + +```{r, result02_data} +#Loading LIBS dataset +libs.df <- readRDS("/academics/MATP-4910-F24/DAR-Mars-F24/Data/supercam_libs_moc_loc.Rds") + +suppressWarnings( + libs.uniquetar <- + aggregate(libs.df, list(Target = libs.df$target), mean)) + +#Aggregate data +libs.uniquetar <- libs.uniquetar %>% select(!c(target,point)) + +#Add the total alkali column (y) +libs_alksil <- libs.df %>% + select(c(SiO2, TiO2, Al2O3, FeOT, MgO, CaO, Na2O, K2O)) %>% + mutate(y = Na2O + K2O) + +#Same fro aggregate data +libs_alksilag <- libs.uniquetar %>% + select(c(SiO2, TiO2, Al2O3, FeOT, MgO, CaO, Na2O, K2O)) %>% + mutate(y = Na2O + K2O) +``` + +### Analysis: Methods and Results + +After getting the total alkali vs silica data for each sample, I need to plot them with a scatter plot. I decided to add a lot of segments and annotations to the graph in order to create the igneous rock classification diagram. +I got the placements for the diagram from https://www2.tulane.edu/~sanelson/eens212/igrockclassif.htm. + +```{r, result02_analysis} +#Drop every column except Silicon and Alkali content +libs_alksil <- libs_alksil %>% + select(c(SiO2, y)) + +libs_alksilag <- libs_alksilag %>% + select(c(SiO2, y)) + +#Cluster them according to the kmeans from the Ternary plot +libs_alksil <- cbind(libs_alksil, cluster=as.factor(tern.km$cluster)) + +libs_alksilag <- cbind(libs_alksilag, cluster=as.factor(tern.km2$cluster)) + +#Plot for original LIBS data +ggplot() + + geom_point(data = libs_alksil, + mapping = aes(x=SiO2, y=y, color=as.character(cluster)), + #add alpha so that labels on graph are visible + alpha = 0.3) + + #Add Line segments and labels for the igneous rocks reference + geom_segment(aes(x=41,y=0, xend=41, yend=7)) + + geom_segment(aes(x=45,y=0, xend=45, yend=5)) + + geom_segment(aes(x=52,y=0, xend=52, yend=5)) + + geom_segment(aes(x=57,y=1, xend=57, yend=6)) + + geom_segment(aes(x=53,y=9, xend=57, yend=6)) + + geom_segment(aes(x=48.5,y=11.5, xend=53, yend=9)) + + geom_segment(aes(x=63,y=2, xend=63, yend=7)) + + geom_segment(aes(x=52,y=5, xend=69, yend=8)) + + geom_segment(aes(x=69,y=8, xend=73, yend=3)) + + geom_segment(aes(x=69,y=8, xend=69, yend=13)) + + geom_segment(aes(x=41,y=3, xend=45, yend=3)) + + geom_segment(aes(x=45,y=5, xend=52, yend=5)) + + geom_segment(aes(x=45,y=5, xend=61, yend=13)) + + geom_segment(aes(x=49.3,y=7.2, xend=52, yend=5)) + + geom_segment(aes(x=45,y=9.4, xend=49.3, yend=7.2)) + + geom_segment(aes(x=41,y=7, xend=52.7, yend=14)) + + geom_segment(aes(x=58,y=11.6, xend=63, yend=7)) + + geom_segment(aes(x=58,y=11.6, xend=49, yend=15.5)) + + annotate("text",x=43,y=1.5,label="Picro-\nbasalt", size = 2) + + annotate("text",x=43.1,y=6.7,label="Tephrite", size = 2) + + annotate("text",x=43.3,y=5.7,label="Basanite", size = 2) + + annotate("text",x=48,y=3.5,label="Basalt", size = 2) + + annotate("text",x=39,y=10,label="Foidite", size = 2) + + annotate("text",x=42,y=14,label="Trachy-\nbasalt", size = 2) + + #to point at the correct area + geom_segment(aes(x=42,y=12.6, xend=49, yend=5.8), color="red") + + annotate("text",x=54.6,y=3.5,label="Basaltic\nandesite", size = 2) + + annotate("text",x=60,y=4.6,label="Andesite", size = 2) + + annotate("text",x=48.5,y=10,label="Phono-", size = 2) + + annotate("text",x=48.5,y=9,label="Tephrite", size = 2) + + annotate("text",x=47,y=18,label="Basaltic\ntrachy-\nandesite", size = 2) + + geom_segment(aes(x=47,y=15.5, xend=53, yend=6.5), color="red") + + annotate("text",x=53,y=11.8,label="Tephri-\nphonolite", size = 2) + + annotate("text",x=57.4,y=8.8,label="Trachy-\nandesite", size = 2) + + annotate("text",x=67,y=5,label="Dacite", size = 2) + + annotate("text",x=72,y=8.5,label="Rhyolite", size = 2) + + annotate("text",x=65,y=9,label="Trachydacite", size = 2) + + annotate("text",x=62.5,y=11.5,label="Trachydacite", size = 2) + + annotate("text",x=56.5,y=14.5,label="Phonolite", size = 2) + + theme_minimal() + + xlim(0,78) + + ylim(-1,38) + + labs(title = "Total Alkali vs. Silica Plot for LIBS", + x = "Si", + y = "Na + K", + color="Cluster") + +#Plot for aggregate data +ggplot() + + geom_point(data = libs_alksilag, + mapping = aes(x=SiO2, y=y, color=as.character(cluster)), + alpha = 0.3) + + geom_segment(aes(x=41,y=0, xend=41, yend=7)) + + geom_segment(aes(x=45,y=0, xend=45, yend=5)) + + geom_segment(aes(x=52,y=0, xend=52, yend=5)) + + geom_segment(aes(x=57,y=1, xend=57, yend=6)) + + geom_segment(aes(x=53,y=9, xend=57, yend=6)) + + geom_segment(aes(x=48.5,y=11.5, xend=53, yend=9)) + + geom_segment(aes(x=63,y=2, xend=63, yend=7)) + + geom_segment(aes(x=52,y=5, xend=69, yend=8)) + + geom_segment(aes(x=69,y=8, xend=73, yend=3)) + + geom_segment(aes(x=69,y=8, xend=69, yend=13)) + + geom_segment(aes(x=41,y=3, xend=45, yend=3)) + + geom_segment(aes(x=45,y=5, xend=52, yend=5)) + + geom_segment(aes(x=45,y=5, xend=61, yend=13)) + + geom_segment(aes(x=49.3,y=7.2, xend=52, yend=5)) + + geom_segment(aes(x=45,y=9.4, xend=49.3, yend=7.2)) + + geom_segment(aes(x=41,y=7, xend=52.7, yend=14)) + + geom_segment(aes(x=58,y=11.6, xend=63, yend=7)) + + geom_segment(aes(x=58,y=11.6, xend=49, yend=15.5)) + + annotate("text",x=43,y=1.5,label="Picro-\nbasalt", size = 2) + + annotate("text",x=43.1,y=6.7,label="Tephrite", size = 2) + + annotate("text",x=43.3,y=5.7,label="Basanite", size = 2) + + annotate("text",x=48,y=3.5,label="Basalt", size = 2) + + annotate("text",x=39,y=10,label="Foidite", size = 2) + + annotate("text",x=42,y=14,label="Trachy-\nbasalt", size = 2) + + #to point at the correct area + geom_segment(aes(x=42,y=12.6, xend=49, yend=5.8), color="red") + + annotate("text",x=54.6,y=3.5,label="Basaltic\nandesite", size = 2) + + annotate("text",x=60,y=4.6,label="Andesite", size = 2) + + annotate("text",x=48.5,y=10,label="Phono-", size = 2) + + annotate("text",x=48.5,y=9,label="Tephrite", size = 2) + + annotate("text",x=47,y=18,label="Basaltic\ntrachy-\nandesite", size = 2) + + geom_segment(aes(x=47,y=15.5, xend=53, yend=6.5), color="red") + + annotate("text",x=53,y=11.8,label="Tephri-\nphonolite", size = 2) + + annotate("text",x=57.4,y=8.8,label="Trachy-\nandesite", size = 2) + + annotate("text",x=67,y=5,label="Dacite", size = 2) + + annotate("text",x=72,y=8.5,label="Rhyolite", size = 2) + + annotate("text",x=65,y=9,label="Trachydacite", size = 2) + + annotate("text",x=62.5,y=11.5,label="Trachydacite", size = 2) + + annotate("text",x=56.5,y=14.5,label="Phonolite", size = 2) + + theme_minimal() + + xlim(0,78) + + ylim(-5,38) + + labs(title = "Total Alkali vs. Silica Plot for LIBS Aggregated by Target", + x = "Si", + y = "Na + K", + color="Cluster") +``` + +### Discussion of results + +From the plot of the original data, we see that Cluster 1 (red) mostly falls in the picrobasalt to basalt category, with some samples in Tephrite Basanite and to the left and right. Cluster 4 (purple) falls around the same categories, but also includes Basaltic Andesite, Andesite, Dacite, Trachybasalt, and Basaltic trachyandesite. There are also some samples in Phonollite and Foidite, which tells me that Cluster 4 has a lot of variation in rock type. Clusters 2 (green) and 3 (blue) are both off of this classification diagram. + + +## Analysis: Question 3: Log Scaling LIBS + +### Question being asked + +I wanted to investigate how log scaling affected the LIBS data and its clustering. + +### Data Preparation + +I prepare the LIBS data set to be scaled twice, once one all of the points and once on the aggregated LIBS dataset we have been using earlier. + +```{r, result03_data} +#Loading LIBS dataset +libs.df <- readRDS("/academics/MATP-4910-F24/DAR-Mars-F24/Data/supercam_libs_moc_loc.Rds") + +suppressWarnings( + libs.uniquetar <- + aggregate(libs.df[], list(Target = libs.df$target), mean)) + +#Aggregate data +libs.uniquetar <- libs.uniquetar %>% select(!c(target,point)) + +#Select only necessary columns +libs_trim <- libs.df %>% select(c(target, SiO2, TiO2, Al2O3, FeOT, MgO, CaO, Na2O, K2O, sol)) +libs_agtrim <- libs.uniquetar %>% select(c(Target, SiO2, TiO2, Al2O3, FeOT, MgO, CaO, Na2O, K2O)) + +#create unscaled data for reference +unscaled_libs <- libs_trim %>% select(!c(target, sol)) + +#Log scale the data sets +log_libs <- log(libs_trim %>% select(!c(target, sol))) +log_libsag <- log(libs_agtrim %>% select(!c(Target))) +``` + +I made the choice of setting all values which are negative infinity in our log scaled data set (meaning they were 0 in the original data set) to -99 (meaning they would be ~0 in the original data set). This allows me to plot all the points from the LIBS data. + +```{r} +log_libs[log_libs == "-Inf"] <- -99 +log_libsag[log_libsag == "-Inf"] <- -99 +``` + +### Analysis methods used + +Just to see if we can learn anything about the log scaled data set I am going to perform Principle Component Analysis (PCA) on all three unscaled, log scaled, and log scaled aggregated by target data sets to see if we can analyze any differences between them. To supplement PCA, I am going to run the elbow test on the data sets, run kmeans with the optimal number of clusters, plot the clusters on heatmaps, and then run PCA on the data sets and plot the pca on a biplot for each data set. + +I start by preforming the elbow test on the data sets. + +```{r, result03_analysis} +# + +# 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)$tot.withinss} + ggplot(data=wss,aes(x=cluster,y=quality)) + + geom_line() +} + +wssplot(unscaled_libs, nc=8, seed=2)+ + ggtitle("Quality of k-means by Cluster for Unscaled LIBS") +wssplot(log_libs, nc=8, seed=2) + + ggtitle("Quality of k-means by Cluster for Log Scaled LIBS") +wssplot(log_libsag, nc=8, seed=2) + + ggtitle("Quality of k-means by Cluster for Log Scaled LIBS Aggregated by Target") +``` + + +I decide on using 4 clusters for each group, just so it is easier to compare to unscaled and the log scaled graphs. I am thinking the aggregate data might reveal something about the data set based on the fact their variance is mostly explained by a similar number of clusters. + +```{r} +set.seed(1234) +kmun <- kmeans(unscaled_libs,4) + +pca_unlibs <- prcomp(unscaled_libs, scale=FALSE) + +clusterun.df<-data.frame(cluster= 1:4, size=kmun$size) +kable(clusterun.df,caption="Samples per cluster") + +pheatmap(kmun$centers,scale="none", main="Clusters by Element Composition on Unscaled LIBS (wt %)") + +km <- kmeans(log_libs,4) + +cluster.df<-data.frame(cluster= 1:4, size=km$size) +kable(cluster.df,caption="Samples per cluster") + +pheatmap(km$centers,scale="none", main="Clusters by Element Composition on Log Scaled LIBS (log(wt %))") + +kmag <- kmeans(log_libsag,4) + +clusterag.df<-data.frame(cluster= 1:4, size=kmag$size) +kable(clusterag.df,caption="Samples per cluster") + +pheatmap(kmag$centers,scale="none", main="Clusters by Element Composition on Log Scaled LIBS Aggregated (log(wt %))") +``` + +Biplot of the PCA on all three data sets: + +```{r} +pca_unlibs <- prcomp(unscaled_libs, scale=FALSE) + +ggbiplot::ggbiplot(pca_unlibs, + groups = as.factor(kmun$cluster)) + + labs(title="Biplot of PCA on Unscaled LIBS") + +pca_libs <- prcomp(log_libs, scale=FALSE) + +ggbiplot::ggbiplot(pca_libs, + groups = as.factor(km$cluster)) + + labs(title="Biplot of PCA on Log LIBS") + + xlim(-2,2) + ylim(-1,9) + +pca_libsag <- prcomp(log_libsag, scale=FALSE) + +ggbiplot::ggbiplot(pca_libsag, + groups = as.factor(kmag$cluster)) + + labs(title="Biplot of PCA on Log LIBS Aggregated by Target") + + xlim(-4,2) + ylim(-10,1) +``` + + + +### Discussion of results + +After looking at the biplots, we see that there is not a lot that the log scaled data sets tell us about any of the clusters or LIBS points in general. The aggregate data is pretty unreadable, and we see no distinction between any of the clusters in the log scaled data in terms of elemental composition. + +From the heatmaps, we don't really see a difference from the other clusters, except for clusters 4 and 2 in the log scaled data. Cluster 4 has a lot less Potassium than the other clusters, and that is why we see it away from the other points. Cluster 2 has a slightly different composition than the other clusters, but it consists of far fewer points, and thus I feel not very informative. + +## Analysis: Question 4: What do we not know about LIBS? + +### Question being asked + +I wanted to investigate other research papers about LIBS to see if it can give us more understanding of the dataset. + +### What I found + +The first thing I wanted to investigate was why the elemental compositions of each sample did not add up to 100, meaning that 100% o the rock has been identified. For some samples, the sum of the elemental compositions can be in the low 80s or as high as 120s. This variance seems to throw the accuracy of all the measurements into question, so I wanted to see why exactly this occurs. + +In the paper Application of Laser-Induced Breakdown Spectroscopy for Depth Profiling of Multilayer and Graded Materials (https://www.mdpi.com/1996-1944/16/20/6641), in section 5 the authors discuss how LIBS data can be hard to analyze in situations where traditional calibration techniques cannot be used, such as remote sensing in space missions, which is the exact situation the data is collected from. In this situation, a calibration free method is used to determine elemental composition, which necessitates several specific criteria. The problem is that with matrix effects, laser parameters, and experimental configurations, it is hard to be completely accurate with analyzing concentrations. + +Some of the difficulty also comes from the fact that the LIBS system itself is not the same every time. From Post-landing Major Element Quantification Using SuperCam Laser Induced Breakdown Spectroscopy (https://www.sciencedirect.com/science/article/pii/S0584854721003049), it is revealed that the LIBS laser is not exactly the same every time it is fired. There can be changes with the size of the ablation, which is essentially the mini crater left behind by the laser. The temperature of the plasma in the laser can vary as well, varying from fire to fire of the laser. These changes can affect the calibration free model for LIBS elemental analysis, which can cuase the issues with total elemental composition as we see. + +## Analysis: Question 5: LIBS on Earth Referece Data + +### Question being asked + +How does the Earth reference data change LIBS samples? + +### Data Preparation + +The Earth reference data we get is in terms of quartiles, and thus we can scale and plot the Mars LIBS data on the Earth reference data. We do this by subtracting the median of the earth reference data from each sample in the LIBS data and dividing by the interquartile range for each element. + +```{r} +# Include all data processing code (if necessary), clearly commented +libs.df <- readRDS("/academics/MATP-4910-F24/DAR-Mars-F24/Data/supercam_libs_moc_loc.Rds") +libs_earth <- readRDS("/academics/MATP-4910-F24/DAR-Mars-F24/Data/LIBS_training_set_quartiles.Rds") + +libs_trim <- libs.df %>% select(c(target, SiO2, TiO2, Al2O3, FeOT, MgO, CaO, Na2O, K2O, sol)) %>% + rowwise() %>% mutate(Si= (SiO2-libs_earth[3,2])/(libs_earth[4,2] - libs_earth[2,2]), + Ti= (TiO2-libs_earth[3,3])/(libs_earth[4,3] - libs_earth[2,3]), + Al= (Al2O3-libs_earth[3,4])/(libs_earth[4,4] - libs_earth[2,4]), + Fe= (FeOT-libs_earth[3,5])/(libs_earth[4,5] - libs_earth[2,5]), + Mg= (MgO-libs_earth[3,6])/(libs_earth[4,6] - libs_earth[2,6]), + Ca= (CaO-libs_earth[3,7])/(libs_earth[4,7] - libs_earth[2,7]), + Na= (Na2O-libs_earth[3,8])/(libs_earth[4,8] - libs_earth[2,8]), + K= (K2O-libs_earth[3,9])/(libs_earth[4,9] - libs_earth[2,9])) %>% + select(!c(SiO2, TiO2, Al2O3, FeOT, MgO, CaO, Na2O, K2O, target, sol)) +``` + +### Analysis: Methods and results + +In order to visualize the scaled data, I will start with a violin plot and then run PCA on the scaled data, repeating all the same steps as we did in Question 3. + +```{r} +ggplot() + + geom_violin(aes(y = libs_trim$Si$SiO2, x = "Si"), fill = "blue") + + geom_violin(aes(y = libs_trim$Ti$TiO2, x = "Ti"), fill = "red") + + geom_violin(aes(y = libs_trim$Al$Al2O3, x = "Al"), fill = "green") + + geom_violin(aes(y = libs_trim$Fe$FeOT, x = "Fe"), fill = "orange") + + geom_violin(aes(y = libs_trim$Mg$MgO, x = "Mg"), fill = "yellow") + + geom_violin(aes(y = libs_trim$Ca$CaO, x = "Ca"), fill = "grey") + + geom_violin(aes(y = libs_trim$Na$Na2O, x = "Na"), fill = "cyan") + + geom_violin(aes(y = libs_trim$K$K2O, x = "K"), fill = "gold") + + labs(title = "Distribution of LIBS Data Scaled on Earth Quartiles", y = "Scaled Value", x = "Element") + + theme_minimal() +``` + + +```{r} +set.seed(1234) +km <- kmeans(libs_trim,4) + +cluster.df<-data.frame(cluster= 1:4, size=km$size) +kable(cluster.df,caption="Samples per cluster") + +pheatmap(km$centers,scale="none", main="Clusters by Element Composition on Earth Scaled LIBS") +``` + +```{r} +pca_libs <- prcomp(libs_trim, scale=FALSE) + +ggbiplot::ggbiplot(pca_libs, + groups = as.factor(km$cluster)) + + labs(title="Biplot of PCA on Earth Scaled LIBS") +``` + +### Discussion of results + +From the heatmap we can see that Cluster 3 is the most different from all the other clusters, as it does not have any amount of Fe or Mg, as compared to the other clusters. Cluster 2 is the cluster most heavily associated with Mg, while Cluster 4 is the most heavily associated with Fe. + +The biplot confirms our understandings from the heatmap. From the data, Cluster 4 seems to be the more different when compared to the other clusters. + +## Analysis: Question 6: Removing Earth Reference Samples + +### Question being asked + +I wanted to look at Margo's LIBS dataset labeled by whether the row is a sample or Earth Reference data, and see how it changes my graphs. + +### Data Preparation + +I am going to prepare my data the exact same way as I did for Questions 1 and 2, but instead I will be using the "libs_typed" data set in the StudentData folder. I am not going to aggregate the LIBS data by target this time. + +```{r} +# Data Processing for the Ternary Graph + +# Load the saved LIBS data with metadata added (libs without earth) +libswe <- readRDS("~/DAR-Mars-F24/StudentData/libs_typed.Rds") + +#Get rid of all earth samples +libswe <- libswe %>% filter(`earthsample?` != 1) + +#Sum the elements we are looking at +libswe <- libswe %>% + mutate(y = (FeOT + MgO) / 100, z = (CaO+Na2O+K2O) / 100, x = (SiO2 + Al2O3) / 100) + +#Data Processing for the Alk Sil Plot + +#Add the total alkali column (y) +libs_alksil <- libswe %>% + select(c(SiO2, TiO2, Al2O3, FeOT, MgO, CaO, Na2O, K2O)) %>% + mutate(y = Na2O + K2O) +``` + +### Analysis: Methods and results + +Just repeating the same analysis from Questions 1 and 2. + +```{r} +#CODE FOR TERNARY + +libs_ternplot <- libswe %>% select(c(x,y,z)) + +set.seed(1234) + +#kmeans on the original data +tern.km <- kmeans(libs_ternplot, centers=4) + +libs_ternplot <- cbind(libs_ternplot, LIBS_Cluster=as.factor(tern.km$cluster)) + +#ternary plot for LIBS data +ggtern(libs_ternplot, ggtern::aes(x=x, y=y, z=z, cluster=LIBS_Cluster)) + + #color by cluster + geom_point(aes(color=LIBS_Cluster), alpha = 0.5) + + theme_rgbw() + + labs(title="Mars 2020 LIBS Ternary Plot with PIXL Data", + subtitle="LIBS data Clustered by Cation Group with PIXL samples by Rock Type \nWith Earth Reference Data Removed", + x="Si+Al2", + y="Fe+Mg", + z="Ca+Na2+K2") + + #suppress warnings here because of some warning with aes() + #add PIXL samples - atmospheric onto the ternary plot + suppressWarnings(geom_point( + data=pixl_ternary, ggtern::aes(x=x, y=y, z=z, + cluster=PIXL_Rock_Type, shape=PIXL_Rock_Type), + size = 2)) + + #Add labels to PIXL data corresponding to sample number + suppressWarnings(geom_text(data=pixl_ternary, + ggtern::aes(x=x, y=y, z=z, label=Sample_display, cluster=PIXL_Rock_Type, + hjust = ifelse(x > 0.43, 1, -0.1), # Horizontal adjust to avoid overlap + vjust = ifelse(x == 0.3668, 1.3, + ifelse(x == 0.375, 1, ifelse(x > 0.43, 1.5, -0.3))), + fontface="bold"), + size=2.7)) + +``` + + +```{r} +#CODE FOR TAS PLOT + +#Drop every column except Silicon and Alkali content +libs_alksil <- libs_alksil %>% + select(c(SiO2, y)) + +#Cluster them according to the kmeans from the Ternary plot +libs_alksil <- cbind(libs_alksil, cluster=as.factor(tern.km$cluster)) + +libs_alksilag <- cbind(libs_alksilag, cluster=as.factor(tern.km2$cluster)) + +#Plot for original LIBS data +ggplot() + + geom_point(data = libs_alksil, + mapping = aes(x=SiO2, y=y, color=as.character(cluster)), + #add alpha so that labels on graph are visible + alpha = 0.3) + + #Add Line segments and labels for the igneous rocks reference + geom_segment(aes(x=41,y=0, xend=41, yend=7)) + + geom_segment(aes(x=45,y=0, xend=45, yend=5)) + + geom_segment(aes(x=52,y=0, xend=52, yend=5)) + + geom_segment(aes(x=57,y=1, xend=57, yend=6)) + + geom_segment(aes(x=53,y=9, xend=57, yend=6)) + + geom_segment(aes(x=48.5,y=11.5, xend=53, yend=9)) + + geom_segment(aes(x=63,y=2, xend=63, yend=7)) + + geom_segment(aes(x=52,y=5, xend=69, yend=8)) + + geom_segment(aes(x=69,y=8, xend=73, yend=3)) + + geom_segment(aes(x=69,y=8, xend=69, yend=13)) + + geom_segment(aes(x=41,y=3, xend=45, yend=3)) + + geom_segment(aes(x=45,y=5, xend=52, yend=5)) + + geom_segment(aes(x=45,y=5, xend=61, yend=13)) + + geom_segment(aes(x=49.3,y=7.2, xend=52, yend=5)) + + geom_segment(aes(x=45,y=9.4, xend=49.3, yend=7.2)) + + geom_segment(aes(x=41,y=7, xend=52.7, yend=14)) + + geom_segment(aes(x=58,y=11.6, xend=63, yend=7)) + + geom_segment(aes(x=58,y=11.6, xend=49, yend=15.5)) + + annotate("text",x=43,y=1.5,label="Picro-\nbasalt", size = 2) + + annotate("text",x=43.1,y=6.7,label="Tephrite", size = 2) + + annotate("text",x=43.3,y=5.7,label="Basanite", size = 2) + + annotate("text",x=48,y=3.5,label="Basalt", size = 2) + + annotate("text",x=39,y=10,label="Foidite", size = 2) + + annotate("text",x=42,y=14,label="Trachy-\nbasalt", size = 2) + + #to point at the correct area + geom_segment(aes(x=42,y=12.6, xend=49, yend=5.8), color="red") + + annotate("text",x=54.6,y=3.5,label="Basaltic\nandesite", size = 2) + + annotate("text",x=60,y=4.6,label="Andesite", size = 2) + + annotate("text",x=48.5,y=10,label="Phono-", size = 2) + + annotate("text",x=48.5,y=9,label="Tephrite", size = 2) + + annotate("text",x=47,y=18,label="Basaltic\ntrachy-\nandesite", size = 2) + + geom_segment(aes(x=47,y=15.5, xend=53, yend=6.5), color="red") + + annotate("text",x=53,y=11.8,label="Tephri-\nphonolite", size = 2) + + annotate("text",x=57.4,y=8.8,label="Trachy-\nandesite", size = 2) + + annotate("text",x=67,y=5,label="Dacite", size = 2) + + annotate("text",x=72,y=8.5,label="Rhyolite", size = 2) + + annotate("text",x=65,y=9,label="Trachydacite", size = 2) + + annotate("text",x=62.5,y=11.5,label="Trachydacite", size = 2) + + annotate("text",x=56.5,y=14.5,label="Phonolite", size = 2) + + theme_minimal() + + xlim(0,78) + + ylim(-1,20) + + labs(title = "Total Alkali vs. Silica Plot for LIBS \nWith Earth Reference Data Removed", + x = "Si", + y = "Na + K", + color="Cluster") + +``` + +### Discussion of results + +Comparing the Ternary Plot to the one we had earlier, we see much fewer points int he fringe area of the bottom right, and we now instead of 4 main clusters all next to each other. The outliers now join Cluster 1 with igneous rocks, while the cluster which was the combination of sedimentary and igneous splits into two different clusters, 3 and 4. + +From the Total Alkali Silica plot, we see that Cluster 4 in the old graph is now Cluster 1 with some Cluster 3 and 4 as well, and the Cluster near the top of the Ternary plot is away from all the points in the TAS plot. We also noticed that the outliers from the TAS plot from earlier are now gone with the Earth reference data removed. + + +## Summary and next steps + +I want to look into providing line plots as Professor Bennett requested. I also need to start working on a comprehensive LIBS notebook to summarize my findings so far. + diff --git a/StudentNotebooks/Assignment05/lahira-assignment05.html b/StudentNotebooks/Assignment05/lahira-assignment05.html new file mode 100644 index 0000000..a8c73f9 --- /dev/null +++ b/StudentNotebooks/Assignment05/lahira-assignment05.html @@ -0,0 +1,1362 @@ + + + + + + + + + + + + + + + +DAR F24 Notebook 5 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ + + + + + + + +
+

Weekly Work Summary

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  • RCS ID: Lahira

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  • Project Name: Mars

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  • Summary of work since last week

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    • Log scaled LIBS data set and performed PCA
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    • Did some research on LIBS
    • +
    • Scale LIBS on Earth reference quartiles
    • +
    • Compare old plots with LIBS with earth reference samples +removed
    • +
  • +
  • NEW: Summary of github issues added and worked

    +
      +
    • Worked on Log Scaling the LIBS dataset
    • +
    • Worked on Earth references for LIBS
    • +
    • Worked on Scaling LIBS on Earth References
    • +
    • Worked on Slides for Dr. Rogers
    • +
  • +
  • Summary of github commits

    +
      +
    • branch is dar-lahira
    • +
    • Pulled this notebook (lahira-assignment05.rmd)
    • +
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  • List of presentations, papers, or other outputs

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  • List of references (if necessary)

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  • Indicate any use of group shared code base

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  • Indicate which parts of your described work were done by you or +as part of joint efforts

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+
+
+

Personal Contribution

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  • This entire Notebook from Questions 3-6 were done by me since the +last notebook was due.
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+
+
+

Analysis: Question 1: Exploring LIBS data

+
+

Question being asked

+

I want to figure out what the cation compositions of the samples can +tell us about the LIBS data, and how aggregating the data can change +this picture. I also want to plot the PIXL data onto the LIBS data to +give the PIXL data some context.

+
+
+

Data Preparation

+

Before I prepared the data, I wanted to learn more about LIBS in the +first place to better understand how to use our data. LIBS stands for +Laser-Induced breakdown Spectroscopy, which uses lasers to heat the +surface of sample, and then reads the emitted wavelengths to determine +the concentrations of various elements. However, the laser in LIBS is +not very consistent, so it takes the average of the multiple firings, +which is why there is a standard deviation for each measurement.

+

To start the analysis, I loaded the PIXL and LIBS data frames, and +then took the sums of three specific elemental combinations: Silicon and +Aluminium, Iron and Magnesium, and Calcium, Sodium, and Potassium. We +can try to classify the LIBS samples based on the ratio of these 3 +elements.

+
# PIXL data added
+pixl.df <- readRDS("/academics/MATP-4910-F24/DAR-Mars-F24/Data/samples_pixl_wide.Rds")
+pixl.df[sapply(pixl.df, is.character)] <- lapply(pixl.df[sapply(pixl.df, is.character)], 
+                                       as.factor)
+pixl.df <- pixl.df[2:16,] #Excluding first, atmospheric sample
+
+#PIXL data, with identically reflected compositions
+new_pixl_trim <- pixl.df %>% 
+  dplyr::select(c("Na20","Mgo","Al203","Si02", "K20","Cao","FeO-T", campaign, type)) %>%
+  rename("Na2O"="Na20","MgO"="Mgo","Al2O3"="Al203","SiO2"="Si02","K2O"="K20",
+         "CaO"="Cao","FeOT"="FeO-T")
+#take the sums of the specific elements, and rename type column
+pixl_ternary <- new_pixl_trim %>%
+  mutate(x=(SiO2+Al2O3)/100,y=(FeOT+MgO)/100,z=(CaO+Na2O+K2O)/100, PIXL_Rock_Type = type) %>%
+  select(-c(SiO2,Al2O3,FeOT,MgO,CaO,Na2O,K2O)) %>%
+  drop_na()
+
+#This is for the labels on the Ternary Plot below
+pixl_ternary <- cbind(pixl_ternary, Sample_display=
+                        c("2","3","4,6,7","5,8,9","","","","",
+                          "10,11","","12,13","","14,15","","16"))
+
+# Load the saved LIBS data with locations added
+libs.df <- readRDS("/academics/MATP-4910-F24/DAR-Mars-F24/Data/supercam_libs_moc_loc.Rds")
+
+libs.df$point <- as.numeric(libs.df$point)
+
+#suppressing warnings here because target and point do not get a mean calculated, 
+#but thats is fine as we have the target anyways and point is no longer relevant
+suppressWarnings(
+  libs.uniquetar <- 
+    aggregate(libs.df, list(Target = libs.df$target), mean))
+
+#drop target and point from the data frame
+libs.uniquetar <- libs.uniquetar %>% select(!c(target,point))
+
+#Sum the elements we are looking at
+libs.df <- libs.df %>% 
+  mutate(y = (FeOT + MgO) / 100, z = (CaO+Na2O+K2O) / 100, x = (SiO2 + Al2O3) / 100)
+
+#Same thing but aggregate
+libs.uniquetar <- libs.uniquetar %>% 
+  mutate(y = (FeOT + MgO) / 100, z = (CaO+Na2O+K2O) / 100, x = (SiO2 + Al2O3) / 100)
+
+
+

Analysis: Methods and results

+

I want to create a ternary plot of both the untouched LIBS data, and +a ternary plot of the aggregate data to see if there are any +differences. A ternary plot just is a graph of the relative compositions +of 3 variables. By plotting the LIBS points, and clustering using +kmeans, we can try to group similar samples together to see if they are +all the same or similar rock type. I then plot the PIXL samples onto the +same graph, and then classifying them by either Crater Floor or Delta +Front to help classify those samples. The code for the PIXL data comes +from Nicolas Morawski’s Assignment 3 notebook.

+
#Only select the columns we are going to use
+libs_ternplot <- libs.df %>% select(c(x,y,z))
+libs_ternplot2 <- libs.uniquetar %>% select(c(x,y,z))
+
+set.seed(1234)
+
+#kmeans on the original data
+tern.km <- kmeans(libs_ternplot, centers=4)
+
+libs_ternplot <- cbind(libs_ternplot, LIBS_Cluster=as.factor(tern.km$cluster))
+
+#ternary plot for LIBS data
+ggtern(libs_ternplot, ggtern::aes(x=x, y=y, z=z, cluster=LIBS_Cluster)) +
+  #color by cluster
+  geom_point(aes(color=LIBS_Cluster), alpha = 0.5) +
+  theme_rgbw() +
+  labs(title="Mars 2020 LIBS Ternary Plot with PIXL Data",
+       subtitle="LIBS data Clustered by Cation Group with PIXL samples by Rock Type",
+       x="Si+Al2",
+       y="Fe+Mg",
+       z="Ca+Na2+K2") +
+  #suppress warnings here because of some warning with aes()
+  #add PIXL samples - atmospheric onto the ternary plot
+  suppressWarnings(geom_point(
+    data=pixl_ternary, ggtern::aes(x=x, y=y, z=z, 
+    cluster=PIXL_Rock_Type, shape=PIXL_Rock_Type),
+    size = 2)) +
+  #Add labels to PIXL data corresponding to sample number
+  suppressWarnings(geom_text(data=pixl_ternary,
+            ggtern::aes(x=x, y=y, z=z, label=Sample_display, cluster=PIXL_Rock_Type,
+            hjust = ifelse(x > 0.43, 1, -0.1),   # Horizontal adjust to avoid overlap
+            vjust = ifelse(x == 0.3668, 1.3, 
+                           ifelse(x == 0.375, 1, ifelse(x > 0.43, 1.5, -0.3))),
+            fontface="bold"),
+            size=2.7))
+

+
#kmeans on the aggregate data
+tern.km2 <- kmeans(as.matrix(libs_ternplot2), centers=4)
+
+libs_ternplot2 <- cbind(libs_ternplot2, LIBS_Cluster=as.factor(tern.km2$cluster))
+
+#plot for aggregate data
+ggtern(libs_ternplot2, ggtern::aes(x=x, y=y, z=z,cluster=LIBS_Cluster)) +
+  geom_point(aes(color=LIBS_Cluster), alpha = 0.5) +
+  theme_rgbw() +
+  labs(title="Mars 2020 LIBS Ternary Plot Aggregated by Target with PIXL Data",
+       subtitle="LIBS data Clustered by Cation Group with PIXL samples by Rock Type",
+       x="Si+Al2",
+       y="Fe+Mg",
+       z="Ca+Na2+K2") +
+  suppressWarnings(geom_point(
+    data=pixl_ternary, ggtern::aes(x=x, y=y, z=z, 
+    cluster=PIXL_Rock_Type, shape=PIXL_Rock_Type),
+    size = 2.5)) +
+  suppressWarnings(geom_text(data=pixl_ternary,
+            ggtern::aes(x=x, y=y, z=z, label=Sample_display, cluster=PIXL_Rock_Type,
+            hjust = ifelse(x > 0.43, 1, -0.1),   # Horizontal adjust to avoid overlap
+            vjust = ifelse(x == 0.3668, 1.3, 
+                           ifelse(x == 0.375, 1, ifelse(x > 0.43, 1.5, -0.3))),
+            fontface="bold"),
+            size=2.7))
+

+
+
+

Discussion of results

+

I created two ternary plots, one using the original LIBS dataset, and +the other aggregated by target. Target I believe is the location from +where the sample took place, so I wanted to see if eliminating the noise +from multiple readings could help us identify trends in the data. For +the ternary diagram itself, I chose the element groups from NASA’s +report on PIXL data for its different samples. From the ternary diagram, +we see that most of the samples are high in both Fe+Mg and Al2, and low +in Ca+Na2+K2. The samples that have higher Ca+Na2+K2 tend to have lower +Fe+Mg and much lower Al2. From the clustering we see that cluster one +tends to have high concentration of Si+Al2 and Fe+Mg, and very low +concentrations of Ca+Na2+K2. Cluster 2 is mostly Fe+Mg, with a little +Si+Al2. Cluster 3 is very diverse, but tends to be the samples with +higher concentrations of Ca+Na2. Cluster 4 has higher concentrations of +Si+Al2, wth lesser concentrations of Fe+Mg.

+

When we look at the plot for the aggregate data, we see little +difference in the key clusters of our graph. When ran with multiple +seeds the clustering can group the points in the bottom right of the +graph to different clusters, but I believe the one where they are their +own cluster is the most accurate.

+

Looking at the PIXL data, we see that sedimentary samples tend to be +higher in Fe and Mg and lower in Si and Al, and are associated mostly +with clusters 2 and 3. The igneous samples are the opposite, and appear +in all clusters 1-3.

+
+
+
+

Analysis: Question 2: Further Classifying LIBS

+
+

Question being asked

+

After making a Ternary plot, I still wanted to find out more about +the LIBS samples. I want to make a TAS (Total Alkali Silica) plot, and +use the igneous rock classification diagram to help us identify rocks +from the LIBS samples.

+
+
+

Data Preparation

+

I am going to compare the sum of the alkali elements to the sum of +silica in each libs sample.

+

I load the LIBS data and select only the columns I want. I also make +the aggregate data again, and select the columns I want from that data +as well. I also add a column, y= Na2O + K2O, which should be the total +alkali content of the LIBS samples.

+
#Loading LIBS dataset
+libs.df <- readRDS("/academics/MATP-4910-F24/DAR-Mars-F24/Data/supercam_libs_moc_loc.Rds")
+
+suppressWarnings(
+  libs.uniquetar <- 
+    aggregate(libs.df, list(Target = libs.df$target), mean))
+
+#Aggregate data
+libs.uniquetar <- libs.uniquetar %>% select(!c(target,point))
+
+#Add the total alkali column (y)
+libs_alksil <- libs.df %>%
+  select(c(SiO2, TiO2, Al2O3, FeOT, MgO, CaO, Na2O, K2O)) %>%
+  mutate(y = Na2O + K2O)
+
+#Same fro aggregate data
+libs_alksilag <- libs.uniquetar %>%
+  select(c(SiO2, TiO2, Al2O3, FeOT, MgO, CaO, Na2O, K2O)) %>%
+  mutate(y = Na2O + K2O)
+
+
+

Analysis: Methods and Results

+

After getting the total alkali vs silica data for each sample, I need +to plot them with a scatter plot. I decided to add a lot of segments and +annotations to the graph in order to create the igneous rock +classification diagram. I got the placements for the diagram from https://www2.tulane.edu/~sanelson/eens212/igrockclassif.htm.

+
#Drop every column except Silicon and Alkali content
+libs_alksil <- libs_alksil %>%
+  select(c(SiO2, y))
+
+libs_alksilag <- libs_alksilag %>%
+  select(c(SiO2, y))
+
+#Cluster them according to the kmeans from the Ternary plot
+libs_alksil <- cbind(libs_alksil, cluster=as.factor(tern.km$cluster))
+
+libs_alksilag <- cbind(libs_alksilag, cluster=as.factor(tern.km2$cluster))
+
+#Plot for original LIBS data
+ggplot() +
+  geom_point(data = libs_alksil,
+             mapping = aes(x=SiO2, y=y, color=as.character(cluster)),
+             #add alpha so that labels on graph are visible
+             alpha = 0.3) + 
+  #Add Line segments and labels for the igneous rocks reference
+  geom_segment(aes(x=41,y=0, xend=41, yend=7)) +
+  geom_segment(aes(x=45,y=0, xend=45, yend=5)) +
+  geom_segment(aes(x=52,y=0, xend=52, yend=5)) +
+  geom_segment(aes(x=57,y=1, xend=57, yend=6)) +
+  geom_segment(aes(x=53,y=9, xend=57, yend=6)) +
+  geom_segment(aes(x=48.5,y=11.5, xend=53, yend=9)) +
+  geom_segment(aes(x=63,y=2, xend=63, yend=7)) +
+  geom_segment(aes(x=52,y=5, xend=69, yend=8)) +
+  geom_segment(aes(x=69,y=8, xend=73, yend=3)) +
+  geom_segment(aes(x=69,y=8, xend=69, yend=13)) +
+  geom_segment(aes(x=41,y=3, xend=45, yend=3)) +
+  geom_segment(aes(x=45,y=5, xend=52, yend=5)) +
+  geom_segment(aes(x=45,y=5, xend=61, yend=13)) +
+  geom_segment(aes(x=49.3,y=7.2, xend=52, yend=5)) +
+  geom_segment(aes(x=45,y=9.4, xend=49.3, yend=7.2)) +
+  geom_segment(aes(x=41,y=7, xend=52.7, yend=14)) +
+  geom_segment(aes(x=58,y=11.6, xend=63, yend=7)) +
+  geom_segment(aes(x=58,y=11.6, xend=49, yend=15.5)) +
+  annotate("text",x=43,y=1.5,label="Picro-\nbasalt", size = 2) +
+  annotate("text",x=43.1,y=6.7,label="Tephrite", size = 2) +
+  annotate("text",x=43.3,y=5.7,label="Basanite", size = 2) +
+  annotate("text",x=48,y=3.5,label="Basalt", size = 2) +
+  annotate("text",x=39,y=10,label="Foidite", size = 2) +
+  annotate("text",x=42,y=14,label="Trachy-\nbasalt", size = 2) +
+  #to point at the correct area
+  geom_segment(aes(x=42,y=12.6, xend=49, yend=5.8), color="red") + 
+  annotate("text",x=54.6,y=3.5,label="Basaltic\nandesite", size = 2) +
+  annotate("text",x=60,y=4.6,label="Andesite", size = 2) +
+  annotate("text",x=48.5,y=10,label="Phono-", size = 2) +
+  annotate("text",x=48.5,y=9,label="Tephrite", size = 2) +
+  annotate("text",x=47,y=18,label="Basaltic\ntrachy-\nandesite", size = 2) +
+  geom_segment(aes(x=47,y=15.5, xend=53, yend=6.5), color="red") +
+  annotate("text",x=53,y=11.8,label="Tephri-\nphonolite", size = 2) +
+  annotate("text",x=57.4,y=8.8,label="Trachy-\nandesite", size = 2) +
+  annotate("text",x=67,y=5,label="Dacite", size = 2) +
+  annotate("text",x=72,y=8.5,label="Rhyolite", size = 2) +
+  annotate("text",x=65,y=9,label="Trachydacite", size = 2) +
+  annotate("text",x=62.5,y=11.5,label="Trachydacite", size = 2) +
+  annotate("text",x=56.5,y=14.5,label="Phonolite", size = 2) +
+  theme_minimal() +
+  xlim(0,78) + 
+  ylim(-1,38) + 
+  labs(title = "Total Alkali vs. Silica Plot for LIBS",
+       x = "Si", 
+       y = "Na + K", 
+       color="Cluster")
+

+
#Plot for aggregate data
+ggplot() +
+  geom_point(data = libs_alksilag,
+             mapping = aes(x=SiO2, y=y, color=as.character(cluster)),
+             alpha = 0.3) +
+  geom_segment(aes(x=41,y=0, xend=41, yend=7)) +
+  geom_segment(aes(x=45,y=0, xend=45, yend=5)) +
+  geom_segment(aes(x=52,y=0, xend=52, yend=5)) +
+  geom_segment(aes(x=57,y=1, xend=57, yend=6)) +
+  geom_segment(aes(x=53,y=9, xend=57, yend=6)) +
+  geom_segment(aes(x=48.5,y=11.5, xend=53, yend=9)) +
+  geom_segment(aes(x=63,y=2, xend=63, yend=7)) +
+  geom_segment(aes(x=52,y=5, xend=69, yend=8)) +
+  geom_segment(aes(x=69,y=8, xend=73, yend=3)) +
+  geom_segment(aes(x=69,y=8, xend=69, yend=13)) +
+  geom_segment(aes(x=41,y=3, xend=45, yend=3)) +
+  geom_segment(aes(x=45,y=5, xend=52, yend=5)) +
+  geom_segment(aes(x=45,y=5, xend=61, yend=13)) +
+  geom_segment(aes(x=49.3,y=7.2, xend=52, yend=5)) +
+  geom_segment(aes(x=45,y=9.4, xend=49.3, yend=7.2)) +
+  geom_segment(aes(x=41,y=7, xend=52.7, yend=14)) +
+  geom_segment(aes(x=58,y=11.6, xend=63, yend=7)) +
+  geom_segment(aes(x=58,y=11.6, xend=49, yend=15.5)) +
+  annotate("text",x=43,y=1.5,label="Picro-\nbasalt", size = 2) +
+  annotate("text",x=43.1,y=6.7,label="Tephrite", size = 2) +
+  annotate("text",x=43.3,y=5.7,label="Basanite", size = 2) +
+  annotate("text",x=48,y=3.5,label="Basalt", size = 2) +
+  annotate("text",x=39,y=10,label="Foidite", size = 2) +
+  annotate("text",x=42,y=14,label="Trachy-\nbasalt", size = 2) +
+  #to point at the correct area
+  geom_segment(aes(x=42,y=12.6, xend=49, yend=5.8), color="red") + 
+  annotate("text",x=54.6,y=3.5,label="Basaltic\nandesite", size = 2) +
+  annotate("text",x=60,y=4.6,label="Andesite", size = 2) +
+  annotate("text",x=48.5,y=10,label="Phono-", size = 2) +
+  annotate("text",x=48.5,y=9,label="Tephrite", size = 2) +
+  annotate("text",x=47,y=18,label="Basaltic\ntrachy-\nandesite", size = 2) +
+  geom_segment(aes(x=47,y=15.5, xend=53, yend=6.5), color="red") +
+  annotate("text",x=53,y=11.8,label="Tephri-\nphonolite", size = 2) +
+  annotate("text",x=57.4,y=8.8,label="Trachy-\nandesite", size = 2) +
+  annotate("text",x=67,y=5,label="Dacite", size = 2) +
+  annotate("text",x=72,y=8.5,label="Rhyolite", size = 2) +
+  annotate("text",x=65,y=9,label="Trachydacite", size = 2) +
+  annotate("text",x=62.5,y=11.5,label="Trachydacite", size = 2) +
+  annotate("text",x=56.5,y=14.5,label="Phonolite", size = 2) +
+  theme_minimal() +
+  xlim(0,78) +
+  ylim(-5,38) +
+  labs(title = "Total Alkali vs. Silica Plot for LIBS Aggregated by Target",
+       x = "Si",
+       y = "Na + K",
+       color="Cluster")
+

+
+
+

Discussion of results

+

From the plot of the original data, we see that Cluster 1 (red) +mostly falls in the picrobasalt to basalt category, with some samples in +Tephrite Basanite and to the left and right. Cluster 4 (purple) falls +around the same categories, but also includes Basaltic Andesite, +Andesite, Dacite, Trachybasalt, and Basaltic trachyandesite. There are +also some samples in Phonollite and Foidite, which tells me that Cluster +4 has a lot of variation in rock type. Clusters 2 (green) and 3 (blue) +are both off of this classification diagram.

+
+
+
+

Analysis: Question 3: Log Scaling LIBS

+
+

Question being asked

+

I wanted to investigate how log scaling affected the LIBS data and +its clustering.

+
+
+

Data Preparation

+

I prepare the LIBS data set to be scaled twice, once one all of the +points and once on the aggregated LIBS dataset we have been using +earlier.

+
#Loading LIBS dataset
+libs.df <- readRDS("/academics/MATP-4910-F24/DAR-Mars-F24/Data/supercam_libs_moc_loc.Rds")
+
+suppressWarnings(
+  libs.uniquetar <- 
+    aggregate(libs.df[], list(Target = libs.df$target), mean))
+
+#Aggregate data
+libs.uniquetar <- libs.uniquetar %>% select(!c(target,point))
+
+#Select only necessary columns
+libs_trim <- libs.df %>% select(c(target, SiO2, TiO2, Al2O3, FeOT, MgO, CaO, Na2O, K2O, sol))
+libs_agtrim <- libs.uniquetar %>% select(c(Target, SiO2, TiO2, Al2O3, FeOT, MgO, CaO, Na2O, K2O))
+
+#create unscaled data for reference
+unscaled_libs <- libs_trim %>% select(!c(target, sol))
+
+#Log scale the data sets
+log_libs <- log(libs_trim %>% select(!c(target, sol)))
+log_libsag <- log(libs_agtrim %>% select(!c(Target)))
+

I made the choice of setting all values which are negative infinity +in our log scaled data set (meaning they were 0 in the original data +set) to -99 (meaning they would be ~0 in the original data set). This +allows me to plot all the points from the LIBS data.

+
log_libs[log_libs == "-Inf"] <- -99
+log_libsag[log_libsag == "-Inf"] <- -99
+
+
+

Analysis methods used

+

Just to see if we can learn anything about the log scaled data set I +am going to perform Principle Component Analysis (PCA) on all three +unscaled, log scaled, and log scaled aggregated by target data sets to +see if we can analyze any differences between them. To supplement PCA, I +am going to run the elbow test on the data sets, run kmeans with the +optimal number of clusters, plot the clusters on heatmaps, and then run +PCA on the data sets and plot the pca on a biplot for each data set.

+

I start by preforming the elbow test on the data sets.

+
#
+
+# 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()
+}
+
+wssplot(unscaled_libs, nc=8, seed=2)+ 
+    ggtitle("Quality of k-means by Cluster for Unscaled LIBS")
+

+
wssplot(log_libs, nc=8, seed=2) + 
+    ggtitle("Quality of k-means by Cluster for Log Scaled LIBS")
+

+
wssplot(log_libsag, nc=8, seed=2) + 
+    ggtitle("Quality of k-means by Cluster for Log Scaled LIBS Aggregated by Target")
+

+

I decide on using 4 clusters for each group, just so it is easier to +compare to unscaled and the log scaled graphs. I am thinking the +aggregate data might reveal something about the data set based on the +fact their variance is mostly explained by a similar number of +clusters.

+
set.seed(1234)
+kmun <- kmeans(unscaled_libs,4)
+
+pca_unlibs <- prcomp(unscaled_libs, scale=FALSE)
+
+clusterun.df<-data.frame(cluster= 1:4, size=kmun$size)
+kable(clusterun.df,caption="Samples per cluster")
+ + + + + + + + + + + + + + + + + + + + + + + + + + +
Samples per cluster
clustersize
1676
2212
329
41015
+
pheatmap(kmun$centers,scale="none", main="Clusters by Element Composition on Unscaled LIBS (wt %)")
+

+
km <- kmeans(log_libs,4)
+
+cluster.df<-data.frame(cluster= 1:4, size=km$size)
+kable(cluster.df,caption="Samples per cluster")
+ + + + + + + + + + + + + + + + + + + + + + + + + + +
Samples per cluster
clustersize
11231
247
3633
421
+
pheatmap(km$centers,scale="none", main="Clusters by Element Composition on Log Scaled LIBS (log(wt %))")
+

+
kmag <- kmeans(log_libsag,4)
+
+clusterag.df<-data.frame(cluster= 1:4, size=kmag$size)
+kable(clusterag.df,caption="Samples per cluster")
+ + + + + + + + + + + + + + + + + + + + + + + + + + +
Samples per cluster
clustersize
12
22
3184
413
+
pheatmap(kmag$centers,scale="none", main="Clusters by Element Composition on Log Scaled LIBS Aggregated (log(wt %))")
+

+

Biplot of the PCA on all three data sets:

+
pca_unlibs <- prcomp(unscaled_libs, scale=FALSE)
+
+ggbiplot::ggbiplot(pca_unlibs,
+                   groups = as.factor(kmun$cluster)) + 
+  labs(title="Biplot of PCA on Unscaled LIBS")
+

+
pca_libs <- prcomp(log_libs, scale=FALSE)
+
+ggbiplot::ggbiplot(pca_libs,
+                   groups = as.factor(km$cluster)) + 
+  labs(title="Biplot of PCA on Log LIBS") + 
+  xlim(-2,2) + ylim(-1,9)
+

+
pca_libsag <- prcomp(log_libsag, scale=FALSE)
+
+ggbiplot::ggbiplot(pca_libsag,
+                   groups = as.factor(kmag$cluster)) + 
+  labs(title="Biplot of PCA on Log LIBS Aggregated by Target") + 
+  xlim(-4,2) + ylim(-10,1)
+

+
+
+

Discussion of results

+

After looking at the biplots, we see that there is not a lot that the +log scaled data sets tell us about any of the clusters or LIBS points in +general. The aggregate data is pretty unreadable, and we see no +distinction between any of the clusters in the log scaled data in terms +of elemental composition.

+

From the heatmaps, we don’t really see a difference from the other +clusters, except for clusters 4 and 2 in the log scaled data. Cluster 4 +has a lot less Potassium than the other clusters, and that is why we see +it away from the other points. Cluster 2 has a slightly different +composition than the other clusters, but it consists of far fewer +points, and thus I feel not very informative.

+
+
+
+

Analysis: Question 4: What do we not know about LIBS?

+
+

Question being asked

+

I wanted to investigate other research papers about LIBS to see if it +can give us more understanding of the dataset.

+
+
+

What I found

+

The first thing I wanted to investigate was why the elemental +compositions of each sample did not add up to 100, meaning that 100% o +the rock has been identified. For some samples, the sum of the elemental +compositions can be in the low 80s or as high as 120s. This variance +seems to throw the accuracy of all the measurements into question, so I +wanted to see why exactly this occurs.

+

In the paper Application of Laser-Induced Breakdown Spectroscopy for +Depth Profiling of Multilayer and Graded Materials (https://www.mdpi.com/1996-1944/16/20/6641), in section 5 +the authors discuss how LIBS data can be hard to analyze in situations +where traditional calibration techniques cannot be used, such as remote +sensing in space missions, which is the exact situation the data is +collected from. In this situation, a calibration free method is used to +determine elemental composition, which necessitates several specific +criteria. The problem is that with matrix effects, laser parameters, and +experimental configurations, it is hard to be completely accurate with +analyzing concentrations.

+

Some of the difficulty also comes from the fact that the LIBS system +itself is not the same every time. From Post-landing Major Element +Quantification Using SuperCam Laser Induced Breakdown Spectroscopy (https://www.sciencedirect.com/science/article/pii/S0584854721003049), +it is revealed that the LIBS laser is not exactly the same every time it +is fired. There can be changes with the size of the ablation, which is +essentially the mini crater left behind by the laser. The temperature of +the plasma in the laser can vary as well, varying from fire to fire of +the laser. These changes can affect the calibration free model for LIBS +elemental analysis, which can cuase the issues with total elemental +composition as we see.

+
+
+
+

Analysis: Question 5: LIBS on Earth Referece Data

+
+

Question being asked

+

How does the Earth reference data change LIBS samples?

+
+
+

Data Preparation

+

The Earth reference data we get is in terms of quartiles, and thus we +can scale and plot the Mars LIBS data on the Earth reference data. We do +this by subtracting the median of the earth reference data from each +sample in the LIBS data and dividing by the interquartile range for each +element.

+
# Include all data processing code (if necessary), clearly commented
+libs.df <- readRDS("/academics/MATP-4910-F24/DAR-Mars-F24/Data/supercam_libs_moc_loc.Rds")
+libs_earth <- readRDS("/academics/MATP-4910-F24/DAR-Mars-F24/Data/LIBS_training_set_quartiles.Rds")
+
+libs_trim <- libs.df %>% select(c(target, SiO2, TiO2, Al2O3, FeOT, MgO, CaO, Na2O, K2O, sol)) %>% 
+  rowwise() %>% mutate(Si= (SiO2-libs_earth[3,2])/(libs_earth[4,2] - libs_earth[2,2]), 
+                       Ti= (TiO2-libs_earth[3,3])/(libs_earth[4,3] - libs_earth[2,3]),
+                       Al= (Al2O3-libs_earth[3,4])/(libs_earth[4,4] - libs_earth[2,4]),
+                       Fe= (FeOT-libs_earth[3,5])/(libs_earth[4,5] - libs_earth[2,5]),
+                       Mg= (MgO-libs_earth[3,6])/(libs_earth[4,6] - libs_earth[2,6]),
+                       Ca= (CaO-libs_earth[3,7])/(libs_earth[4,7] - libs_earth[2,7]),
+                       Na= (Na2O-libs_earth[3,8])/(libs_earth[4,8] - libs_earth[2,8]),
+                       K= (K2O-libs_earth[3,9])/(libs_earth[4,9] - libs_earth[2,9])) %>%
+  select(!c(SiO2, TiO2, Al2O3, FeOT, MgO, CaO, Na2O, K2O, target, sol))
+
+
+

Analysis: Methods and results

+

In order to visualize the scaled data, I will start with a violin +plot and then run PCA on the scaled data, repeating all the same steps +as we did in Question 3.

+
ggplot() +
+  geom_violin(aes(y = libs_trim$Si$SiO2, x = "Si"), fill = "blue") +
+  geom_violin(aes(y = libs_trim$Ti$TiO2, x = "Ti"), fill = "red") +
+  geom_violin(aes(y = libs_trim$Al$Al2O3, x = "Al"), fill = "green") +
+  geom_violin(aes(y = libs_trim$Fe$FeOT, x = "Fe"), fill = "orange") +
+  geom_violin(aes(y = libs_trim$Mg$MgO, x = "Mg"), fill = "yellow") +
+  geom_violin(aes(y = libs_trim$Ca$CaO, x = "Ca"), fill = "grey") +
+  geom_violin(aes(y = libs_trim$Na$Na2O, x = "Na"), fill = "cyan") +
+  geom_violin(aes(y = libs_trim$K$K2O, x = "K"), fill = "gold") +
+  labs(title = "Distribution of LIBS Data Scaled on Earth Quartiles", y = "Scaled Value", x = "Element") +
+  theme_minimal()
+

+
set.seed(1234)
+km <- kmeans(libs_trim,4)
+
+cluster.df<-data.frame(cluster= 1:4, size=km$size)
+kable(cluster.df,caption="Samples per cluster")
+ + + + + + + + + + + + + + + + + + + + + + + + + + +
Samples per cluster
clustersize
1364
2496
3821
4251
+
pheatmap(km$centers,scale="none", main="Clusters by Element Composition on Earth Scaled LIBS")
+

+
pca_libs <- prcomp(libs_trim, scale=FALSE)
+
+ggbiplot::ggbiplot(pca_libs,
+                   groups = as.factor(km$cluster)) + 
+  labs(title="Biplot of PCA on Earth Scaled LIBS")
+

+
+
+

Discussion of results

+

From the heatmap we can see that Cluster 3 is the most different from +all the other clusters, as it does not have any amount of Fe or Mg, as +compared to the other clusters. Cluster 2 is the cluster most heavily +associated with Mg, while Cluster 4 is the most heavily associated with +Fe.

+

The biplot confirms our understandings from the heatmap. From the +data, Cluster 4 seems to be the more different when compared to the +other clusters.

+
+
+
+

Analysis: Question 6: Removing Earth Reference Samples

+
+

Question being asked

+

I wanted to look at Margo’s LIBS dataset labeled by whether the row +is a sample or Earth Reference data, and see how it changes my +graphs.

+
+
+

Data Preparation

+

I am going to prepare my data the exact same way as I did for +Questions 1 and 2, but instead I will be using the “libs_typed” data set +in the StudentData folder. I am not going to aggregate the LIBS data by +target this time.

+
# Data Processing for the Ternary Graph
+
+# Load the saved LIBS data with metadata added (libs without earth)
+libswe <- readRDS("~/DAR-Mars-F24/StudentData/libs_typed.Rds")
+
+#Get rid of all earth samples
+libswe <- libswe %>% filter(`earthsample?` != 1)
+
+#Sum the elements we are looking at
+libswe <- libswe %>%
+  mutate(y = (FeOT + MgO) / 100, z = (CaO+Na2O+K2O) / 100, x = (SiO2 + Al2O3) / 100)
+
+#Data Processing for the Alk Sil Plot
+
+#Add the total alkali column (y)
+libs_alksil <- libswe %>%
+  select(c(SiO2, TiO2, Al2O3, FeOT, MgO, CaO, Na2O, K2O)) %>%
+  mutate(y = Na2O + K2O)
+
+
+

Analysis: Methods and results

+

Just repeating the same analysis from Questions 1 and 2.

+
#CODE FOR TERNARY
+
+libs_ternplot <- libswe %>% select(c(x,y,z))
+
+set.seed(1234)
+
+#kmeans on the original data
+tern.km <- kmeans(libs_ternplot, centers=4)
+
+libs_ternplot <- cbind(libs_ternplot, LIBS_Cluster=as.factor(tern.km$cluster))
+
+#ternary plot for LIBS data
+ggtern(libs_ternplot, ggtern::aes(x=x, y=y, z=z, cluster=LIBS_Cluster)) +
+  #color by cluster
+  geom_point(aes(color=LIBS_Cluster), alpha = 0.5) +
+  theme_rgbw() +
+  labs(title="Mars 2020 LIBS Ternary Plot with PIXL Data",
+       subtitle="LIBS data Clustered by Cation Group with PIXL samples by Rock Type \nWith Earth Reference Data Removed",
+       x="Si+Al2",
+       y="Fe+Mg",
+       z="Ca+Na2+K2") +
+  #suppress warnings here because of some warning with aes()
+  #add PIXL samples - atmospheric onto the ternary plot
+  suppressWarnings(geom_point(
+    data=pixl_ternary, ggtern::aes(x=x, y=y, z=z, 
+    cluster=PIXL_Rock_Type, shape=PIXL_Rock_Type),
+    size = 2)) +
+  #Add labels to PIXL data corresponding to sample number
+  suppressWarnings(geom_text(data=pixl_ternary,
+            ggtern::aes(x=x, y=y, z=z, label=Sample_display, cluster=PIXL_Rock_Type,
+            hjust = ifelse(x > 0.43, 1, -0.1),   # Horizontal adjust to avoid overlap
+            vjust = ifelse(x == 0.3668, 1.3, 
+                           ifelse(x == 0.375, 1, ifelse(x > 0.43, 1.5, -0.3))),
+            fontface="bold"),
+            size=2.7))
+

+
#CODE FOR TAS PLOT
+
+#Drop every column except Silicon and Alkali content
+libs_alksil <- libs_alksil %>%
+  select(c(SiO2, y))
+
+#Cluster them according to the kmeans from the Ternary plot
+libs_alksil <- cbind(libs_alksil, cluster=as.factor(tern.km$cluster))
+
+libs_alksilag <- cbind(libs_alksilag, cluster=as.factor(tern.km2$cluster))
+
+#Plot for original LIBS data
+ggplot() +
+  geom_point(data = libs_alksil,
+             mapping = aes(x=SiO2, y=y, color=as.character(cluster)),
+             #add alpha so that labels on graph are visible
+             alpha = 0.3) + 
+  #Add Line segments and labels for the igneous rocks reference
+  geom_segment(aes(x=41,y=0, xend=41, yend=7)) +
+  geom_segment(aes(x=45,y=0, xend=45, yend=5)) +
+  geom_segment(aes(x=52,y=0, xend=52, yend=5)) +
+  geom_segment(aes(x=57,y=1, xend=57, yend=6)) +
+  geom_segment(aes(x=53,y=9, xend=57, yend=6)) +
+  geom_segment(aes(x=48.5,y=11.5, xend=53, yend=9)) +
+  geom_segment(aes(x=63,y=2, xend=63, yend=7)) +
+  geom_segment(aes(x=52,y=5, xend=69, yend=8)) +
+  geom_segment(aes(x=69,y=8, xend=73, yend=3)) +
+  geom_segment(aes(x=69,y=8, xend=69, yend=13)) +
+  geom_segment(aes(x=41,y=3, xend=45, yend=3)) +
+  geom_segment(aes(x=45,y=5, xend=52, yend=5)) +
+  geom_segment(aes(x=45,y=5, xend=61, yend=13)) +
+  geom_segment(aes(x=49.3,y=7.2, xend=52, yend=5)) +
+  geom_segment(aes(x=45,y=9.4, xend=49.3, yend=7.2)) +
+  geom_segment(aes(x=41,y=7, xend=52.7, yend=14)) +
+  geom_segment(aes(x=58,y=11.6, xend=63, yend=7)) +
+  geom_segment(aes(x=58,y=11.6, xend=49, yend=15.5)) +
+  annotate("text",x=43,y=1.5,label="Picro-\nbasalt", size = 2) +
+  annotate("text",x=43.1,y=6.7,label="Tephrite", size = 2) +
+  annotate("text",x=43.3,y=5.7,label="Basanite", size = 2) +
+  annotate("text",x=48,y=3.5,label="Basalt", size = 2) +
+  annotate("text",x=39,y=10,label="Foidite", size = 2) +
+  annotate("text",x=42,y=14,label="Trachy-\nbasalt", size = 2) +
+  #to point at the correct area
+  geom_segment(aes(x=42,y=12.6, xend=49, yend=5.8), color="red") + 
+  annotate("text",x=54.6,y=3.5,label="Basaltic\nandesite", size = 2) +
+  annotate("text",x=60,y=4.6,label="Andesite", size = 2) +
+  annotate("text",x=48.5,y=10,label="Phono-", size = 2) +
+  annotate("text",x=48.5,y=9,label="Tephrite", size = 2) +
+  annotate("text",x=47,y=18,label="Basaltic\ntrachy-\nandesite", size = 2) +
+  geom_segment(aes(x=47,y=15.5, xend=53, yend=6.5), color="red") +
+  annotate("text",x=53,y=11.8,label="Tephri-\nphonolite", size = 2) +
+  annotate("text",x=57.4,y=8.8,label="Trachy-\nandesite", size = 2) +
+  annotate("text",x=67,y=5,label="Dacite", size = 2) +
+  annotate("text",x=72,y=8.5,label="Rhyolite", size = 2) +
+  annotate("text",x=65,y=9,label="Trachydacite", size = 2) +
+  annotate("text",x=62.5,y=11.5,label="Trachydacite", size = 2) +
+  annotate("text",x=56.5,y=14.5,label="Phonolite", size = 2) +
+  theme_minimal() +
+  xlim(0,78) + 
+  ylim(-1,20) + 
+  labs(title = "Total Alkali vs. Silica Plot for LIBS \nWith Earth Reference Data Removed",
+       x = "Si", 
+       y = "Na + K", 
+       color="Cluster")
+

+
+
+

Discussion of results

+

Comparing the Ternary Plot to the one we had earlier, we see much +fewer points int he fringe area of the bottom right, and we now instead +of 4 main clusters all next to each other. The outliers now join Cluster +1 with igneous rocks, while the cluster which was the combination of +sedimentary and igneous splits into two different clusters, 3 and 4.

+

From the Total Alkali Silica plot, we see that Cluster 4 in the old +graph is now Cluster 1 with some Cluster 3 and 4 as well, and the +Cluster near the top of the Ternary plot is away from all the points in +the TAS plot. We also noticed that the outliers from the TAS plot from +earlier are now gone with the Earth reference data removed.

+
+
+
+

Summary and next steps

+

I want to look into providing line plots as Professor Bennett +requested. I also need to start working on a comprehensive LIBS notebook +to summarize my findings so far.

+
+ + + + +
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