A Fast deflation Method for Sparse Principal Component Analysis via Subspace Projections

TL;DR

This paper introduces a fast deflation method for sparse PCA that uses subspace projections via Household QR factorization, significantly improving computational efficiency while maintaining key PCA criteria.

Contribution

The paper proposes a novel SPCA-SP method leveraging subspace projections for faster sparse PCA with balanced sparsity, orthogonality, and variance explained.

Findings

Effective on benchmark datasets

Balances sparsity and orthogonality

Reduces computational time significantly

Abstract

The implementation of conventional sparse principal component analysis (SPCA) on high-dimensional data sets has become a time consuming work. In this paper, a series of subspace projections are constructed efficiently by using Household QR factorization. With the aid of these subspace projections, a fast deflation method, called SPCA-SP, is developed for SPCA. This method keeps a good tradeoff between various criteria, including sparsity, orthogonality, explained variance, balance of sparsity, and computational cost. Comparative experiments on the benchmark data sets confirm the effectiveness of the proposed method.