Hybrid Generative/Discriminative Approaches for Proportional Data Modeling and Classification

The work proposed in this paper is motivated by the need to develop powerful models and approaches to classify and learn proportional data. Indeed, an abundance of interesting data in several applications occur naturally in this form. Our goal is to discover and capture the intrinsic nature of the data by proposing some approaches that combine the major advantages of generative models namely finite mixtures and discriminative techniques namely support vector machines (SVMs). Indeed, SVMs often rely on classic kernels which are not generally meaningful for proportional data. One serious limitation of these kernels is that they do not take into account the nature of data to classify and choosing a suitable kernel continues to be a formidable challenge for data mining and machine learning researchers. Our approach builds on selecting accurate kernels generated from finite mixtures of Dirichlet, generalized Dirichlet and Beta-Liouville distributions which chief advantage is their flexibility and explanatory capabilities in the case of heterogenous proportional data. Using extensive simulations and a number of experiments involving scene modeling and classification, and automatic image orientation detection, we show the merits of the proposed mixture models and the accuracy of the generated kernels.