The Alpha-Beta-Symetric Divergence and their Positive Definite Kernel

TL;DR

This paper introduces the Alpha-Beta-Symmetric divergence, a new symmetric Hilbertian metric derived from Alpha-Beta-divergence, along with associated kernels, and demonstrates their application in SVMs and image classification.

Contribution

It proposes a novel symmetric divergence and related kernels, enhancing kernel methods for probability measures and demonstrating their practical utility.

Findings

The ABS-divergence is a valid Hilbertian metric.

The proposed kernels improve SVM performance.

Effective image classification algorithm using the new divergence.

Abstract

In this article we study the field of Hilbertian metrics and positive definit (pd) kernels on probability measures, they have a real interest in kernel methods. Firstly we will make a study based on the Alpha-Beta-divergence to have a Hilbercan metric by proposing an improvement of this divergence by constructing it so that its is symmetrical the Alpha-Beta-Symmetric-divergence (ABS-divergence) and also do some studies on these properties but also propose the kernels associated with this divergence. Secondly we will do mumerical studies incorporating all proposed metrics/kernels into support vector machine (SVM). Finally we presented a algorithm for image classification by using our divergence.