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Adaptation of Gaussian ARD kernel for multiclass classification

The problem of optimizing Gaussian Automatic Relevance (ARD) kernel in a multiclass setting is considered. Unlike the conventional Gaussian kernel with a single width parameter, the Gaussian ARD kernel adopts multiple widths corresponding to the input features. We first present a model selection criterion named kernel distance-based class separability (KDCS) to evaluate the goodness of a kernel in multiclass classification scenario, then propose a gradient-based optimization algorithm to tune the width parameters of Gaussian ARD kernel via maximizing the KDCS criterion. This method is essentially a feature weighting method since each learned parameter indicates the relative importance of the corresponding feature. The proposed method is demonstrated with some UCI machine learning benchmark examples.