NP-Hardness and Inapproximability of Sparse PCA

19 Feb 2015 · Malik Magdon-Ismail ·

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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