A Direct Formulation for Sparse PCA Using Semidefinite Programming
Abstract
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 modifica- tion 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.
Cite
Text
D'aspremont et al. "A Direct Formulation for Sparse PCA Using Semidefinite Programming." Neural Information Processing Systems, 2004.Markdown
[D'aspremont et al. "A Direct Formulation for Sparse PCA Using Semidefinite Programming." Neural Information Processing Systems, 2004.](https://mlanthology.org/neurips/2004/daspremont2004neurips-direct/)BibTeX
@inproceedings{daspremont2004neurips-direct,
title = {{A Direct Formulation for Sparse PCA Using Semidefinite Programming}},
author = {D'aspremont, Alexandre and Ghaoui, Laurent E. and Jordan, Michael I. and Lanckriet, Gert R.},
booktitle = {Neural Information Processing Systems},
year = {2004},
pages = {41-48},
url = {https://mlanthology.org/neurips/2004/daspremont2004neurips-direct/}
}