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}
}
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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