Sparse Principal Components Analysis: a Tutorial

TL;DR

This tutorial introduces Least Squares Sparse Principal Components Analysis (LS SPCA), a simple and effective method for computing sparse, uncorrelated principal components that approximate datasets with fewer variables, offering advantages over other SPCA methods.

Contribution

The paper presents LS SPCA, a new intuitive method for sparse PCA that avoids common drawbacks of existing approaches and is demonstrated on real datasets.

Findings

LS SPCA produces sparse, uncorrelated principal components.

The method is computationally simple and effective.

An R package for LS SPCA is available.

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.