Cluster based RBF Kernel for Support Vector Machines

Abstract: In the classical Gaussian SVM classification we use the feature space projection transforming points to normal distributions with fixed covariance matrices (identity in the standard RBF and the covariance of the whole dataset in Mahalanobis RBF). In this paper we add additional information to Gaussian SVM by considering local geometry-dependent feature space projection. We emphasize that our approach is in fact an algorithm for a construction of the new Gaussian-type kernel. We show that better (compared to standard RBF and Mahalanobis RBF) classification results are obtained in the simple case when the space is preliminary divided by k-means into two sets and points are represented as normal distributions with a covariances calculated according to the dataset partitioning. We call the constructed method C$_k$RBF, where $k$ stands for the amount of clusters used in k-means. We show empirically on nine datasets from UCI repository that C$_2$RBF increases the stability of the grid search (measured as the probability of finding good parameters).