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Frank Vallentin - Sparse PCA and convex optimization

Mathematical Institute, University of Cologne

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Principal component analysis (PCA) is one of the most useful techniques for dimension reduction. However, in situations where one has many variables but only few samples, PCA has the drawback that generally the principal components are linear combination of all variables. In Sparse PCA (SPCA) one limits the number of used variables in the components; this makes the problem NP-hard. One way to approximate SPCA efficiently is the convex optimization approach by d'Aspremont, El Ghaoui, Jordan, and Lanckriet: Here on approximates the sparse components step by step by solving in each step a semidefinite optimization problem and deflating the covariance matrix. In the talk I will give an alternative approach which requires the solution of only one semidefinite optimization problem.