Sparse Principal Components Analysis: a Tutorial

Abstract

The topic of this tutorial is Least Squares Sparse Principal Components Analysis (LS SPCA) which is a simple method for computing approximated Principal Components which are combinations of only a few of the observed variables. Analogously to Principal Components, these components are uncorrelated and sequentially best approximate the dataset. The derivation of LS SPCA is intuitive for anyone familiar with linear regression. Since LS SPCA is based on a different optimality from other SPCA methods and does not suffer from their serious drawbacks. I will demonstrate on two datasets how useful and parsimonious sparse PCs can be computed. An R package for computing LS SPCA is available for download.