Forward Selection Component Analysis: Algorithms and Applications.

Abstract

Principal Component Analysis (PCA) is a powerful and widely used tool for dimensionality reduction. However, the principal components generated are linear combinations of all the original variables and this often makes interpreting results and root-cause analysis difficult. Forward Selection Component Analysis (FSCA) is a recent technique that overcomes this difficulty by performing variable selection and dimensionality reduction at the same time. This paper provides, for the first time, a detailed presentation of the FSCA algorithm, and introduces a number of new variants of FSCA that incorporate a refinement step to improve performance. We then show different applications of FSCA and compare the performance of the different variants with PCA and Sparse PCA. The results demonstrate the efficacy of FSCA as a low information loss dimensionality reduction and variable selection technique and the improved performance achievable through the inclusion of a refinement step.