A Mixed Mahalanobis Kernel for Sparse Bayesian Classification

Relevance vector machine (RVM) is a typical sparse learning model. The most widely used kernel in RVM is Radial Basis Function (RBF), but it is based on the Euclidean distance and don't take the distribution information of training samples into consideration which sometimes leads to a poor performance. Therefore, in this paper, we propose a mixed Mahalanobis kernel for Sparse Bayesian classification which explores the distribution characteristics of data set by means of GMM, and built the kernel matrix based on the weighted Mahalanobis distances from all Gaussian components. The evaluation of the proposed kernel is conducted by means of kernel target alignment (KTA). Applying the proposed kernel to RVM, a new version of RVM, MM-RVM, is formed. The algorithm has been applied to several UCI datasets and the experimental results shows the superior performance of our proposed method and the effectiveness of the mixed Mahalanobis kernel.