On the Quality of a Semidefinite Programming Bound for Sparse Principal Component Analysis
| dc.creator | Ghaoui, Laurent El | |
| dc.date | 2006-01-18 | |
| dc.date | 2006-02-03 | |
| dc.date.accessioned | 2026-07-07T08:07:28Z | |
| dc.date.available | 2026-07-07T08:07:28Z | |
| dc.description | We examine the problem of approximating a positive, semidefinite matrix $Σ$ by a dyad $xx^T$, with a penalty on the cardinality of the vector $x$. This problem arises in sparse principal component analysis, where a decomposition of $Σ$ involving sparse factors is sought. We express this hard, combinatorial problem as a maximum eigenvalue problem, in which we seek to maximize, over a box, the largest eigenvalue of a symmetric matrix that is linear in the variables. This representation allows to use the techniques of robust optimization, to derive a bound based on semidefinite programming. The quality of the bound is investigated using a technique inspired by Nemirovski and Ben-Tal (2002). | |
| dc.description | 13 pages, 3 figures This new version corresponds to an extensive revision of the earlier version | |
| dc.identifier | https://arxiv.org/abs/math/0601448 | |
| dc.identifier | http://arxiv.org/abs/math/0601448 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/130949 | |
| dc.subject | Optimization and Control | |
| dc.subject | Statistics Theory | |
| dc.title | On the Quality of a Semidefinite Programming Bound for Sparse Principal Component Analysis | |
| dc.type | text |