NP-Hardness and Inapproximability of Sparse PCA
classification
💻 cs.LG
cs.CCcs.DSmath.COstat.ML
keywords
sparseexcludereductionalgorithmsapproximationassumptionscliquecomplexity
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We give a reduction from {\sc clique} to establish that sparse PCA is NP-hard. The reduction has a gap which we use to exclude an FPTAS for sparse PCA (unless P=NP). Under weaker complexity assumptions, we also exclude polynomial constant-factor approximation algorithms.
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