A Randomized Rounding Algorithm for Sparse PCA
Kimon Fountoulakis, Abhisek Kundu, Eugenia-Maria Kontopoulou and, Petros Drineas

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.
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Taxonomy
MethodsPrincipal Components Analysis
