NP-Hardness and Inapproximability of Sparse PCA

02/19/2015

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by   Malik Magdon-Ismail, et al.

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We give a reduction from 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.