# A direct formulation for sparse PCA using semidefinite programming

@article{dAspremont2004ADF, title={A direct formulation for sparse PCA using semidefinite programming}, author={Alexandre d'Aspremont and Laurent El Ghaoui and Michael I. Jordan and Gert R. G. Lanckriet}, journal={SIAM Review}, year={2004}, volume={49}, pages={434-448} }

- Published 2004 in NIPS
DOI:10.1137/050645506

Given a covariance matrix, we consider the problem of maximizing the variance explained by a particular linear combination of the input variables while constraining the number of nonzero coefficients in this combination. This problem arises in the decomposition of a covariance matrix into sparse factors or sparse PCA, 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… CONTINUE READING

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