An Adaptive Radial Basis Function Kernel for Support Vector Data Description

For one-class classification or novelty detection, the metric of the feature space is essential for a good performance. Typically, it is assumed that the metric of the feature space is relatively isotropic, or flat, indicating that a distance of 1 can be interpreted in a similar way for every location and direction in the feature space. When this is not the case, thresholds on distances that are fitted in one part of the feature space will be suboptimal for other parts. To avoid this, the idea of this paper is to modify the width parameter in the Radial Basis Function (RBF) kernel for the Support Vector Data Description (SVDD) classifier. Although there have been numerous approaches to learn the metric in a feature space for (supervised) classification problems, for one-class classification this is harder, because the metric cannot be optimized to improve a classification performance. Instead, here we propose to consider the local pairwise distances in the training set. The results obtained on both artificial and real datasets demonstrate the ability of the modified RBF kernel to identify local scales in the input data, extracting its general structure and improving the final classification performance for novelty detection problems.