Certifiably optimal sparse principal component analysis
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12532_2018_153_ReferencePDF.pdf
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Author(s)
Berk, Lauren
Bertsimas, Dimitris
Date Issued
January 1, 2019
Publisher
Springer Berlin Heidelberg
Version
Author's final manuscript
Abstract
Abstract
This paper addresses the sparse principal component analysis (SPCA) problem for covariance matrices in dimension n aiming to find solutions with sparsity k using mixed integer optimization. We propose a tailored branch-and-bound algorithm, Optimal-SPCA, that enables us to solve SPCA to certifiable optimality in seconds for
$$n = 100$$
n
=
100
s,
$$k=10$$
k
=
10
s. This same algorithm can be applied to problems with
$$n=10{,}000\,\mathrm{s}$$
n
=
10
,
000
s
or higher to find high-quality feasible solutions in seconds while taking several hours to prove optimality. We apply our methods to a number of real data sets to demonstrate that our approach scales to the same problem sizes attempted by other methods, while providing superior solutions compared to those methods, explaining a higher portion of variance and permitting complete control over the desired sparsity. The software that was reviewed as part of this submission has been given the DOI (digital object identifier)
https://doi.org/10.5281/zenodo.2027898
.
MIT Department
Massachusetts Institute of Technology. Operations Research Center
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/s12532-018-0153-6
