An iterative coordinate descent algorithm to compute sparse low-rank approximations

TL;DR

This paper introduces an iterative coordinate descent algorithm for efficiently computing sparse low-rank approximations, avoiding explicit covariance matrix computation, and demonstrating effectiveness in data recovery and classification tasks.

Contribution

The paper presents a novel iterative coordinate descent method extending the Kogbetliantz algorithm to compute sparse principal components without explicit covariance matrix formation.

Findings

Effective recovery of sparse principal components on various datasets

Improved dimensionality reduction for classification tasks

Algorithm avoids explicit covariance matrix computation

Abstract

In this paper, we describe a new algorithm to build a few sparse principal components from a given data matrix. Our approach does not explicitly create the covariance matrix of the data and can be viewed as an extension of the Kogbetliantz algorithm to build an approximate singular value decomposition for a few principal components. We show the performance of the proposed algorithm to recover sparse principal components on various datasets from the literature and perform dimensionality reduction for classification applications.