Sparse eigen methods by D.C. programming

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Sparse eigen methods by D.C. programming
Eigenvalue problems are rampant in machine learning and statistics and appear in the context of classification, dimensionality reduction, etc. In this paper, we consider a cardinality constrained variational formulation of generalized eigenvalue problem with sparse principal component analysis (PCA) as a special case. Using 1-norm approximation to the cardinality constraint, previous methods have proposed both convex and non-convex solutions to the sparse PCA problem. In contrast, we propose a tighter approximation that is related to the negative log-likelihood of a Student's t-distribution. The problem is then framed as a d.c. (difference of convex functions) program and is solved as a sequence of locally convex programs. We show that the proposed method not only explains more variance with sparse loadings on the principal directions but also has better scalability compared to other methods. We demonstrate these results on a collection of datasets of varying dimensionality, two ...
Bharath K. Sriperumbudur, David A. Torres, Gert R.
Added 17 Nov 2009
Updated 17 Nov 2009
Type Conference
Year 2007
Where ICML
Authors Bharath K. Sriperumbudur, David A. Torres, Gert R. G. Lanckriet
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