Direct convex relaxations of sparse SVM

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Direct convex relaxations of sparse SVM
Although support vector machines (SVMs) for binary classification give rise to a decision rule that only relies on a subset of the training data points (support vectors), it will in general be based on all available features in the input space. We propose two direct, novel convex relaxations of a nonconvex sparse SVM formulation that explicitly constrains the cardinality of the vector of feature weights. One relaxation results in a quadratically-constrained quadratic program (QCQP), while the second is based on a semidefinite programming (SDP) relaxation. The QCQP formulation can be interpreted as applying an adaptive soft-threshold on the SVM hyperplane, while the SDP formulation learns a weighted inner-product (i.e. a kernel) that results in a sparse hyperplane. Experimental results show an increase in sparsity while conserving the generalization performance compared to a standard as well as a linear programming SVM.
Antoni B. Chan, Nuno Vasconcelos, Gert R. G. Lanck
Added 17 Nov 2009
Updated 17 Nov 2009
Type Conference
Year 2007
Where ICML
Authors Antoni B. Chan, Nuno Vasconcelos, Gert R. G. Lanckriet
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