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.

• Type: Conference
• Year: 2004
• Where: NIPS
• Authors: Alexandre d'Aspremont, Laurent El Ghaoui, Michael I. Jordan, Gert R. G. Lanckriet
• Keywords: Covariance Matrix, NIPS 2004, NIPS 2007, Rank-one Matrix, Semidefinite Symmetric Matrix