This paper introduces an algorithm for the automatic relevance determination of input variables in kernelized Support Vector Machines. Relevance is measured by scale factors defining the input space metric, and feature selection is performed by assigning zero weights to irrelevant variables. The metric is automatically tuned by the minimization of the standard SVM empirical risk, where scale factors are added to the usual set of parameters denning the classifier. Feature selection is achieved by constraints encouraging the sparsity of scale factors. The resulting algorithm compares favorably to state-of-the-art feature selection procedures and demonstrates its effectiveness on a demanding facial expression recognition problem.
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