Sparse Principal Component of a Rank-deficient Matrix

Details Sparse Principal Component of a Rank-deficient Matrix Sparse Principal Component of a Rank-deficient Matrix

2011-06-08

arxiv.org/abs/1106.1651v1

Computer Science

Information Theory

5 pages, 1 figure, to be presented at ISIT

Scientific paper

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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