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

Source: [The Alpha-Beta-Symetric Divergence and their Positive Definite Kernel](<https://www.sota2.com/research/paper/68fa64de1e209131cea06ed4>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T21:12:58.577Z

Authors: Mactar Ndaw, Macoumba Ndour, Papa Ngom

Published: 2018-03-01T18:10:26.000Z

## 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.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1803.00001>)

[PDF](<https://arxiv.org/pdf/1803.00001.pdf>)