Approximation Algorithms for Sparse Principal Component Analysis

Agniva Chowdhury, Petros Drineas, David Woodruff, Samson Zhou

Keywords: Sparse PCA, Principal component analysis, Randomized linear algebra, Singular value decomposition

Abstract: Principal component analysis (PCA) is a widely used dimension reduction technique in machine learning and multivariate statistics. To improve the interpretability of PCA, various approaches to obtain sparse principal direction loadings have been proposed, which are termed Sparse Principal Component Analysis (SPCA). In this paper, we present three provably accurate, polynomial time, approximation algorithms for the SPCA problem, without imposing any restrictive assumptions on the input covariance matrix. The first algorithm is based on randomized matrix multiplication; the second algorithm is based on a novel deterministic thresholding scheme; and the third algorithm is based on a semidefinite programming relaxation of SPCA. All algorithms come with provable guarantees and run in low-degree polynomial time. Our empirical evaluations confirm our theoretical findings.

One-sentence Summary: We present three provably accurate approximation algorithms for the Sparse Principal Component Analysis (SPCA) problem, without imposing any restrictive assumptions on the input covariance matrix.

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