Sparse Principal Component of a Rank-deficient Matrix
Information Theory
2011-06-10 v1 Machine Learning
Systems and Control
math.IT
Optimization and Control
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.
Keywords
Cite
@article{arxiv.1106.1651,
title = {Sparse Principal Component of a Rank-deficient Matrix},
author = {Megasthenis Asteris and Dimitris S. Papailiopoulos and George N. Karystinos},
journal= {arXiv preprint arXiv:1106.1651},
year = {2011}
}
Comments
5 pages, 1 figure, to be presented at ISIT