Introduction to PCA; Cluster analysis and Report Writing in R👨💻
Post Graduate Students, CPEB Club, University of Ibadan
2023-08-19
Agenda
Introduction to PCA; Cluster analysis and Report writing in R
My goal is to make you excited about how to perform this analysis in R!
I will entertain questions at the end
Packages Used Today
Here we are going to focuses on PCA
factoextra.PCAis used to summarize the information contained in a continuous (i.e, quantitative) multivariate data by reducing the dimensionality of the data without loosing important information.
Principal Component Analysis
Principal component analysis (PCA) allows us to summarize and visualize the information in a data set containing individuals/observations described by multiple inter-correlated quantitative variables.
Each variable could be considered as a different dimension.
If you have more than 3 variables in your data sets, it could be very difficult to visualize a multi-dimensional hyperspace.
The goal of PCA is to identify directions (or Principal Components) along which the direction in the data is maximal.
PCA Continuation
Principal component analysis is used to extract the important information from a multivariate data table and to express this information as a set of few new variables called principal components.
These new variables correspond to a linear combination of the originals.
The number of principal components is less than or equal to the number of original variables.
The information in a given data set corresponds to the total variation it contains. The goal of PCA is to identify directions (or principal components) along which the variation in the data is maximal.
PCA is very useful when variable within the dataset are highly correlated.
R packages
Several functions from different packages are available in the R software for computing PCA:
prcomp() and princomp() [built-in R stats package]
PCA() [FactoMineR package]
dudi.pca() [ade4 package]
epPCA() [ExPosition package]
No matter what function you decide to use, you can easily extract and visualize the results of PCA using R functions provided in the factoextra R package.
Install the package as follow:
install.packages(“factoextra”)
Load them in R, by typing this:
library(“factoextra”)
Visualization and Interpretation of PCA Results with factoextra R Package
get_eigenvalue (res.pca): Extract the eigenvalues/variances of principal components.
fviz_eig (res.pca): Visualize the eigenvalues
get_pca_ind (res.pca), get_pca_var : Extract the results for individual and variable respectively.
fviz_pca_ind, fviz_pca_var (res.pca): Visualize the results of individual and variables, respectively.
fviz_pca_biplot (res.pca): Make a biplot of individuals and variables.
Eigenvalues or Variances
The eigenvalues measure the amount of variation retained by each principal component.
The eigenvalues are larger for the first PCs and small for the subsequent PCs.
The first PCs corresponds to the directions with the maximum amount of variation in the data set.
Eigenvalues can be used to determine the number of principal components to retain after PCA (Kaiser, 1961).
An eigenvalue > 1 indicates that PCs account for more variance than accounted by one of the original variables in standardized data. This is commonly used as cutoff point for which PCs are retained.
The above point holds true only when the data are standardized.
Demo on PCA
