A direct formulation for sparse PCA using semidefinite programming
| dc.creator | d'Aspremont, Alexandre | |
| dc.creator | Ghaoui, Laurent El | |
| dc.creator | Jordan, Michael I. | |
| dc.creator | Lanckriet, Gert R. G. | |
| dc.date | 2004-06-16 | |
| dc.date | 2006-05-20 | |
| dc.date.accessioned | 2026-07-07T06:36:37Z | |
| dc.date.available | 2026-07-07T06:36:37Z | |
| dc.description | 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. We also discuss Nesterov's smooth minimization technique applied to the SDP arising in the direct sparse PCA method. | |
| dc.description | Final version, to appear in SIAM review | |
| dc.identifier | https://arxiv.org/abs/cs/0406021 | |
| dc.identifier | http://arxiv.org/abs/cs/0406021 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/100138 | |
| dc.subject | Computational Engineering, Finance, and Science | |
| dc.title | A direct formulation for sparse PCA using semidefinite programming | |
| dc.type | text |