A Randomized Rounding Algorithm for Sparse PCA

TL;DR

This paper introduces a simple two-step randomized rounding algorithm for sparse PCA that approximates the optimal solution with theoretical guarantees and competitive practical performance.

Contribution

The paper proposes a novel two-step approach combining L1 penalization and randomized rounding for sparse PCA, with proven approximation guarantees.

Findings

Guarantees an additive error approximation

Balances sparsity and accuracy effectively

Performs competitively against state-of-the-art tools

Abstract

We present and analyze a simple, two-step algorithm to approximate the optimal solution of the sparse PCA problem. Our approach first solves a L1 penalized version of the NP-hard sparse PCA optimization problem and then uses a randomized rounding strategy to sparsify the resulting dense solution. Our main theoretical result guarantees an additive error approximation and provides a tradeoff between sparsity and accuracy. Our experimental evaluation indicates that our approach is competitive in practice, even compared to state-of-the-art toolboxes such as Spasm.