  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.
