1. PCA/LDA Lab
CSCE 587
Spring 2017

2. PCA/LDA Lab
# Plan A: PCA & LDA Lab # We will need the following packages: # stat # ggplot2 # ggfortify # lfda # # stat & ggplot2 are already installed and can be loaded # ggfortify and lfda are not installed # Install ggfortify --- This will take a while # Install lfda This won't take as long as ggfortify # after installation, load ggfortify & lfda

3. PCA/LDA Lab # Plan B: PCA & LDA Lab
# We will need the following packages:
# stats
# MASS
# ggplot2
# stats, MASS & ggplot2 are already installed and can be loaded
# ggfortify and lfda are not available for the version of R the virtual machines
> install.packages('ggfortify')
Warning in install.packages :
package ‘ggfortify’ is not available (for R version 3.1.3)
> install.packages("lfda")
package ‘lfda’ is not available (for R version 3.1.3)

4. PCA ############################################################
# example iris data
# PCA
# extract the independent variables
iris_data <- iris[,-5]
# generate the PCs
iris_pca <- prcomp(iris_data, center = TRUE, scale. = TRUE)
# Display the PCA object
print(iris_pca)

5. PCA # convert from SD to var # get percent var #plot percent var
tot_var <- sum(sapply(iris_pca$sdev,function(x) x*x))
# get percent var
pct_var <- sapply(iris_pca$sdev,function(x) x*x/tot_var)
#plot percent var
plot(pct_var, type="l")

6. PCA # first two PCs account for most of the variance
sum(pct_var[1:2])
# plot the first two principal components
# If you install ggfortify on you laptop you can use the
# autoplot command that is commented out below o/w
# use the work-around plot command
# autoplot(prcomp(iris_data))
plot(prcomp(iris_data)$x[,1:2])

7. PCA # plot the first two principal components and color by species
# autoplot(prcomp(iris_data), data = iris, colour = 'Species')
plot(prcomp(iris_data)$x[,1:2], col=iris[,5])

8. ggfortify plots for our PCA example
# If you were able to install ggfortify: plot the first two principal
# components, color by species, and label by observation index
autoplot(prcomp(iris_data), data = iris, colour = 'Species', label = TRUE, label.size = 3)

9. ggfortify plots for our PCA example
# If you were able to install ggfortify: plot the first two principal
# components, color by species, and label by observation index
autoplot(prcomp(iris_data), data = iris, colour = 'Species', label = TRUE, label.size = 3)
# If you were able to install ggfortify: plot the first to PCs and draw
# the eigenvectors and label the loadings
autoplot(prcomp(iris_data), data = iris, colour = 'Species', loadings = TRUE, loadings.colour = 'blue',loadings.label = TRUE, loadings.label.size = 3)

10. LDA using the lfda package
########################################################## # If your were able to install lfda you can use the lfda LDA function # Create the LDA model. The first argument is the set of 4 # independent variables. # The second argument is the dependent variable. # The third argument is the dimensionality of the reduced space # The fourth argument is the type of metric in the embedding space # # iris_LDA <- lfda(iris_data, iris[, 5], r = 3, metric="plain")

11. LDA using the lfda package
# If your were able to install lfda & ggfortify: plot the model # autoplot(iris_LDA, data = iris, frame = TRUE, frame.colour = 'Species') # # If your were able to install lfda: plot the model and color the # data by class # autoplot(iris_LDA, data = iris, colour="Species", frame = TRUE, frame.colour = 'Species')

12. LDA from MASS package # Create a data frame for the iris dataset
Iris <- data.frame(rbind(iris3[,,1], iris3[,,2], iris3[,,3]),Sp = rep(c("s","c","v"), rep(50,3)))
# Decide which observations a comprise the training set
train <- sample(1:150, 75)
# Display the class membership of the training data set
table(Iris$Sp[train])

13. LDA from MASS package # create the LDA model
# Formula: SP ~., i.e. Sp is the classification and the other columns
# are the independant data
# Iris is the data set
# prior = c(1,1,1)/3 even priors
# subset: which observations are used to train with
z <- lda(Sp ~ ., Iris, prior = c(1,1,1)/3, subset = train)

14. LDA from MASS package
# project from 4 iris dimensions onto the dimension of the first eigenvector
iris_x <- (z$scaling[,1]) %*% t(iris[,-5])
# project from 4 iris dimensions onto the dimension of the second eigenvector
iris_y <- (z$scaling[,2]) %*% t(iris[,-5])

15. LDA from MASS package # plot 150 iris data points
plot(iris_y~iris_x)
# plot 150 iris data points & color by species
plot(iris_y~iris_x, col=iris[,5])

16. More difficult PCA example
##############################################################
# PCA example using icu data from earlier in the semester
tmp <- icu[,-c(1, 2)]
pca_tmp <- prcomp(tmp, center = TRUE, scale. = TRUE)
print(pca_tmp)
plot(pca_tmp, type="l")
tot_var <- sum(sapply(pca_tmp$sdev,function(x) x*x))

17. More difficult PCA example
pct_var <- sapply(pca_tmp$sdev,function(x) x*x/tot_var)
plot(pct_var, type="l")
sum(pct_var[1:10])
# autoplot(prcomp(tmp))
plot(prcomp(tmp)$x[,1:2])
# autoplot(prcomp(tmp), data = icu, colour = 'STA')
plot(prcomp(tmp)$x[,1:2], col=icu[,2]+1)