The Sparse Principal Component Analysis Problem: Optimality Conditions and Algorithms

Amir Beck () and Yakov Vaisbourd ()
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Amir Beck: Technion
Yakov Vaisbourd: Technion

Journal of Optimization Theory and Applications, 2016, vol. 170, issue 1, No 9, 119-143

Abstract: Abstract Sparse principal component analysis addresses the problem of finding a linear combination of the variables in a given dataset with a sparse coefficients vector that maximizes the variability of the data. This model enhances the ability to interpret the principal components and is applicable in a wide variety of fields including genetics and finance, just to name a few. We suggest a necessary coordinate-wise-based optimality condition and show its superiority over the stationarity-based condition that is commonly used in the literature, which is the basis for many of the algorithms designed to solve the problem. We devise algorithms that are based on the new optimality condition and provide numerical experiments that support our assertion that algorithms, which are guaranteed to converge to stronger optimality conditions, perform better than algorithms that converge to points satisfying weaker optimality conditions.

Keywords: Optimality conditions; Principal component analysis; Sparsity constrained problems; Stationarity; Numerical methods (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-016-0934-x

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