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.

1o pages, 11 figures