Spectral measures for kernel matrices comparison

Abstract

With the emergence of data fusion techniques (kernel combinations, ensemble methods and boosting algorithms), the task of comparing distance/similarity/ kernel matrices is becoming increasingly relevant. However, the choice of an appropriate metric for matrices involved in pattern recognition problems is far from trivial. In this work we propose a general spectral framework to build metrics for matrix spaces. Within the general framework of matrix pencils, we propose a new metric for symmetric and semi-positive definite matrices, called Pencil Distance (PD). The generality of our approach is demonstrated by showing that the Kernel Alignment (KA) measure is a particular case of our spectral approach. We illustrate the performance of the proposed measures using some classification problems. © Springer-Verlag Berlin Heidelberg 2007.