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In this paper, we investigate the problem of training support vector machines (SVMs) on count data. Multinomial generalized Dirichlet mixture models allow us to model efficiently count data. On the other hand, SVMs permit good discrimination. We propose, then, a hybrid model that appropriately combines their advantages. Finite mixture models are introduced, as an SVM kernel, to incorporate prior knowledge about the nature of data involved in the problem at hand. In the context of this model, we compare different kernels. Through an application involving image database categorization, we find that our data-driven kernel performs better.