A Kernel Between Unordered Sets of Data: The Gaussian Mixture Approach

Abstract

In this paper, we present a new kernel for unordered sets of data of the same type. It works by first fitting a set with a Gaussian mixture, then evaluate an efficient kernel on the two fitted Gaussian mixtures. Furthermore, we show that this kernel can be extended to sets embedded in a feature space implicitly defined by another kernel, where Gaussian mixtures are fitted with the kernelized EM algorithm [6], and the kernel for Gaussian mixtures are modified to use the outputs from the kernelized EM. All computation depends on data only through their inner products as evaluations of the base kernel. The kernel is computable in closed form, and being able to work in a feature space improves its flexibility and applicability. Its performance is evaluated in experiments on both synthesized and real data.