PCA - Example

# PCA tuto: http://www.sthda.com/english/wiki/principal-component-analysis-how-to-reveal-the-most-important-variables-in-your-data-r-software-and-data-mining

# Marie de Léséleuc Feb 2016

rm(list = ls())
#install.packages("reshape")
#install.packages("multcomp")
#install.packages("vcd")
#install.packages("Rcpp")
#install.packages("FactoMineR")

library(reshape)
library(multcomp)
library(vcd)
library(Rcpp)
library(FactoMineR)

# setting path to access my csv file
setwd("C:\\Users\\mdeleseleuc\\Documents")
mydata<- read.csv(file="PCA.csv",head=TRUE,sep=";")
mydata <- mydata[1:8,]
head(mydata)

str(mydata)

# remove undesirable dimensions from mydata and cast dimensions as numerical or categorical (factor)

mydata.sub <- mydata[,2:length(mydata)]

for (i in 1:2) {
  mydata.sub[,i] <- as.factor(mydata.sub[,i])
} 

for (i in 3:166) {
  mydata.sub[,i] <- as.numeric(mydata.sub[,i])
} 

str(mydata.sub)

# variable are numbered to refer to them in PCA

var.rank <- data.frame(Variable = names(mydata.sub), Rank = 1:166)

# Summary data
summary(mydata.sub)

# Run PCA 
mydata.sub.pca <- PCA(mydata.sub, scale.unit = TRUE, quali.sup = 1:2, graph=FALSE)
summary(mydata.sub.pca)

  # 4 first dimensions account for 68% of variance
  # 5 first dimensions account for 80% of variance  

# Proportion of variation retained by the PCs

eigenvalues <- mydata.sub.pca$eig
head(eigenvalues[, 1:2])

# Visualization of importance of PCs

library(devtools)
install_github("kassambara/factoextra")
library("factoextra")
fviz_screeplot(mydata.sub.pca, ncp=7)

# Take a look at the important dimensions
summary(mydata.sub.pca, nbelement=166, ncp=5) # ncp = 5 since 5 first dim account for 80% of variance

head(mydata.sub.pca$var$cos2)

dimdesc(mydata.sub.pca, axe =1)
dimdesc(mydata.sub.pca, axe =2)
dimdesc(mydata.sub.pca, axe =3)
dimdesc(mydata.sub.pca, axe =4)
dimdesc(mydata.sub.pca, axe =5)


# Coordinates of variables
head(mydata.sub.pca$var$coord)
fviz_pca_var(mydata.sub.pca)

plot(mydata.sub.pca, choix='var', cex=.7, axes=c(1,2), new.plot = TRUE , xlim=range(-1:1), ylim=range(-1:1))
plot(mydata.sub.pca, choix='var', cex=.7, axes=c(3,4), new.plot = TRUE , xlim=range(-1:1), ylim=range(-1:1))


# Quality of the representation for var.

head(mydata.sub.pca$var$cos2)

  # The closer to the circle of correlations, the better

fviz_pca_var(mydata.sub.pca, col.var="cos2") +
  scale_color_gradient2(low="white", mid="blue", 
                        high="red", midpoint=0.5) + theme_minimal()

# Contribution of the variables to the principal component

 # The highest the contribution with the first PCs, the more important the var. 
head(mydata.sub.pca$var$contrib, 10)

 # most important variables: 

 # var. above red line = important to component
 # Contribution to PC1

x <- fviz_contrib(mydata.sub.pca, choice = "var", axes = 1) 
mydata.sub.pca.PC1.var <- data.frame(x$data[which(x$data$val > 0.75),1]) # 0.75 = red line

 # Contribution to PC2

y <- fviz_contrib(mydata.sub.pca, choice = "var", axes = 2)
mydata.sub.pca.PC2.var <- data.frame(y$data[which(y$data$val > 0.67),1])

 # Total contribution on PC1 and PC2
z <- fviz_contrib(mydata.sub.pca, choice = "var", axes = 1:2)
mydata.sub.pca.PC1PC2.var <- data.frame(z$data[which(z$data$val > 37),1])

 # Show only important variables

fviz_contrib(mydata.sub.pca, choice = "var", axes = 1, top = 50)
fviz_contrib(mydata.sub.pca, choice = "var", axes = 2, top = 50)

 # Control variable colors using their contributions
fviz_pca_var(mydata.sub.pca, col.var="contrib")

# Change the gradient color
 fviz_pca_var(mydata.sub.pca, col.var="contrib") +
   scale_color_gradient2(low="white", mid="blue", 
                         high="red", midpoint=50) + theme_minimal()

# Dimension description

 # Use dimdesc() to identify the most correlated var. with a given PC

pca.desc <- dimdesc(mydata.sub.pca, axes = c(1,2,3,4))
# Description of dimension 1
x <- pca.desc$Dim.1
str(x)

x <- list(x)
x <- na.omit(x)
x <- x[order(x$quanti.p.value),]

# Description of dimension 2
pca.desc$Dim.2

# Description of dimension 3
pca.desc$Dim.3

# Cos2 : quality of the representation for individuals on the principal components

 # The squared cosine shows the importance of a component for a given observation.

fviz_pca_ind(mydata.sub.pca, col.ind="cos2") +
  scale_color_gradient2(low="white", mid="blue", 
                        high="red", midpoint=0.50) + theme_minimal()

# Contribution of the individuals to the princial components 

 # The most contributing individuals associated with a given PC can be visualized as follow :
  
  # Contributions of individuals to PC1
  fviz_pca_contrib(mydata.sub.pca, choice = "ind", axes = 1)

# Clustering 

mydata.sub.pca.hcpc <- HCPC(mydata.sub.pca)

names(mydata.sub.pca.hcpc)
mydata.sub.pca.hcpc$desc.var
# Description of dimension 4
pca.desc$Dim.4