Optimal Sparse Linear Encoders and Sparse PCA

Part of Advances in Neural Information Processing Systems 29 (NIPS 2016)

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Malik Magdon-Ismail, Christos Boutsidis


Principal components analysis~(PCA) is the optimal linear encoder of data. Sparse linear encoders (e.g., sparse PCA) produce more interpretable features that can promote better generalization. (\rn{1}) Given a level of sparsity, what is the best approximation to PCA? (\rn{2}) Are there efficient algorithms which can achieve this optimal combinatorial tradeoff? We answer both questions by providing the first polynomial-time algorithms to construct \emph{optimal} sparse linear auto-encoders; additionally, we demonstrate the performance of our algorithms on real data.