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NIPS
2004

A Direct Formulation for Sparse PCA Using Semidefinite Programming

9 years 23 days ago
A Direct Formulation for Sparse PCA Using Semidefinite Programming
We examine the problem of approximating, in the Frobenius-norm sense, a positive, semidefinite symmetric matrix by a rank-one matrix, with an upper bound on the cardinality of its eigenvector. The problem arises in the decomposition of a covariance matrix into sparse factors, and has wide applications ranging from biology to finance. We use a modification of the classical variational representation of the largest eigenvalue of a symmetric matrix, where cardinality is constrained, and derive a semidefinite programming based relaxation for our problem.
Alexandre d'Aspremont, Laurent El Ghaoui, Michael
Added 31 Oct 2010
Updated 31 Oct 2010
Type Conference
Year 2004
Where NIPS
Authors Alexandre d'Aspremont, Laurent El Ghaoui, Michael I. Jordan, Gert R. G. Lanckriet
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