## On the Quality of a Semidefinite Programming Bound for Sparse Principal Component Analysis**Download:**http://arxiv.org/abs/math/0601448.
**Author:**L. El Ghaoui.
**Status:**Preprint on arXiv.
**Abstract:**We examine the problem of approximating a positive, semidefinite matrix by a dyad , with a penalty on the cardinality of the vector . This problem arises in sparse principal component analysis, where a decomposition of 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).
**Related entries:**A. d'Aspremont, F. Bach, L. El Ghaoui. Optimal Solutions for Sparse Principal Component Analysis.
**Bibtex reference:**
@unpublished{Elg:06, Author = {L. {El Ghaoui}}, Month = {February}, Note = {arXiv:math/060144}, Title = {On the Quality of a Semidefinite Programming Bound for Sparse Principal Component Analysis}, Year = {2006}} |