FactoMineR

What are we using FactoMineR and factoextra for?

• Performing Principal Components Analysis with FactoMineR

• Visualizing it in a ggplot2 framework with factoextra

# install.packages("FactoMineR")
# install.packages("factoextra")

library(FactoMineR)
library(ggplot2)
library(factoextra)

## Welcome! Related Books: `Practical Guide To Cluster Analysis in R` at https://goo.gl/13EFCZ

What do we need to know about PCA?

• Summarizes the information present in a multivariate data set by transforming the set of observations into a data set of synthetic, linearly uncorrelated variables called principal components (PCs).

• Ranks the PCs in order of how much variation they explain, so the first PC explains the most of the variation, the second PC explains the second most amount of the variation, etc.

• Reduces the dimensionality of a multivariate dataset while losing the least amount of information possible (ideally you only have to look at 2 or 3 of the PCs but still see most of the important information).

A Simple Example

PCA

data("iris") # built in data set
head(iris) # 4 continuous variables and 1 categorical variable

##   Sepal.Length Sepal.Width Petal.Length Petal.Width Species
## 1          5.1         3.5          1.4         0.2  setosa
## 2          4.9         3.0          1.4         0.2  setosa
## 3          4.7         3.2          1.3         0.2  setosa
## 4          4.6         3.1          1.5         0.2  setosa
## 5          5.0         3.6          1.4         0.2  setosa
## 6          5.4         3.9          1.7         0.4  setosa

# make a new dataset that only has the continuous variables
# we will use the Species later
iris2 <- iris[1:4]
head(iris2)

##   Sepal.Length Sepal.Width Petal.Length Petal.Width
## 1          5.1         3.5          1.4         0.2
## 2          4.9         3.0          1.4         0.2
## 3          4.7         3.2          1.3         0.2
## 4          4.6         3.1          1.5         0.2
## 5          5.0         3.6          1.4         0.2
## 6          5.4         3.9          1.7         0.4

# PCA analysis to get PCs
iris.pca <- PCA(iris2, scale.unit = TRUE, graph = FALSE)

# look at eigenvalues (measure of how much variance is contained in a PC)
# there are the same number of PCs as original variables
iris.pca$eig

##        eigenvalue percentage of variance cumulative percentage of variance
## comp 1 2.91849782             72.9624454                          72.96245
## comp 2 0.91403047             22.8507618                          95.81321
## comp 3 0.14675688              3.6689219                          99.48213
## comp 4 0.02071484              0.5178709                         100.00000

Scree plot

# Scree plot with factoextra
fviz_screeplot(iris.pca, ncp = 4) # ncp = number of PCs to show

Plots with individuals and contributions of variables

# Simple PCA factor map with FactoMineR graphics
plot.PCA(iris.pca, axes = c(1,2), choix = "var")

# shows us the directions of the contributions of the original variables
# variables pointing the same direction are correlated with each other

# Biplot with factoextra
# Biplot means it has individuals and contributions
fviz_pca(iris.pca)

# include only contributions of variables to clean it up
fviz_pca_var(iris.pca, col.var = "contrib")

# Control scale colors
fviz_pca_var(iris.pca, col.var = "contrib") +
  scale_color_gradient2(low = "blue", mid = "steelblue", high = "red", midpoint = 25.0) +
  theme_void()

# include only individuals with no labels
fviz_pca_ind(iris.pca, label = "none")

# use Species from iris to change habillage
fviz_pca_ind(iris.pca, label="none", habillage = iris$Species)

# changed color and shape

# add ellipses
fviz_pca_ind(iris.pca, label="none", habillage = iris$Species,
             addEllipses = TRUE, ellipse.level = 0.95)

Biplot

# Make a pretty biplot
fviz_pca_biplot(iris.pca,
                # individuals
                geom.ind = "point",
                fill.ind = iris$Species, col.ind = "black",
                pointshape = 21, pointsize = 2,
                addEllipses = TRUE,
                # variables
                col.var = "contrib",
                gradient.cols = "RdYlBu",
                legend.title = list(fill = "Species",
                                    color = "Contrib",
                                    alpha = "Contrib")) +
  scale_color_gradient2(low = "blue", mid = "steelblue", high = "red", midpoint = 25.0)

## Scale for 'colour' is already present. Adding another scale for
## 'colour', which will replace the existing scale.