A Randomized Rounding Algorithm for Sparse PCA

Kimon Fountoulakis; Abhisek Kundu; Eugenia-Maria Kontopoulou; Petros Drineas

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arXiv · 1508.03337

A Randomized Rounding Algorithm for Sparse PCA

Kimon Fountoulakis·Abhisek Kundu·Eugenia-Maria Kontopoulou·Petros Drineas

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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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Kimon Fountoulakis, Abhisek Kundu, Eugenia-Maria Kontopoulou, Petros Drineas. 2015-08-13. A Randomized Rounding Algorithm for Sparse PCA. https://arxiv.org/abs/1508.03337

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