Radius-Margin Ratio Optimization for Dot-Product Boolean Kernel Learning

Abstract

It is known that any dot-product kernel can be seen as a linear non-negative combination of homogeneous polynomial kernels. In this paper, we demonstrate that, under mild conditions, any dot-product kernel defined on binary valued data can be seen as a linear non-negative combination of boolean kernels, specifically, monotone conjunctive kernels (mC-kernels) with different degrees. We also propose a new radius-margin based multiple kernel learning (MKL) algorithm to learn the parameters of the combination. An empirical analysis of the MKL weights distribution shows that our method is able to give solutions which are more sparse and effective compared to the ones of state-of-the-art margin-based MKL methods. The empirical analysis have been performed on eleven UCI categorical datasets.