Sparse Principal Component of a Rank-deficient Matrix

Megasthenis Asteris; Dimitris S. Papailiopoulos; George N. Karystinos

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arXiv · 1106.1651

Sparse Principal Component of a Rank-deficient Matrix

Megasthenis Asteris·Dimitris S. Papailiopoulos·George N. Karystinos

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Abstract

We consider the problem of identifying the sparse principal component of a rank-deficient matrix. We introduce auxiliary spherical variables and prove that there exists a set of candidate index-sets (that is, sets of indices to the nonzero elements of the vector argument) whose size is polynomially bounded, in terms of rank, and contains the optimal index-set, i.e. the index-set of the nonzero elements of the optimal solution. Finally, we develop an algorithm that computes the optimal sparse principal component in polynomial time for any sparsity degree.

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Megasthenis Asteris, Dimitris S. Papailiopoulos, George N. Karystinos. 2011-06-08. Sparse Principal Component of a Rank-deficient Matrix. https://arxiv.org/abs/1106.1651

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