Simultaneous learning of localized multiple kernels and classifier with weighted regularization

Abstract

Kernel classifiers have demonstrated their high performance for many classification problems. For the proper selection of kernel functions, multiple kernel learning (MKL) has been researched. Furthermore, the localized MKL (LMKL) enables to set the weights for the kernel functions at each point. However, the training of the weight functions for kernel functions is a complex nonlinear problem and a classifier can be trained separately after the weights are fixed. The iteration of the two processes are often necessary. In this paper we propose a new framework for MKL/LMKL. In the framework, not kernel functions but mappings to the feature space are combined with weights. We also propose a new learning scheme to train simultaneously weights for kernel functions and a classifier. We realize a classifier by our framework with the Gaussian kernel function and the support vector machine. Finally, we show its advantages by experimental results. © 2012 Springer-Verlag Berlin Heidelberg.