Abstract

Recently Inverted Beta-Liouville mixture models have emerged as an efficient paradigm for proportional positive vectors modeling and unsupervised learning. However, little attention has been devoted to investigate these generative models within discriminative classifiers. Our aim here is to reveal the structure of non-Gaussian data by generating new probabilistic SVM kernels from inverted-Beta Liouville mixture models. The inverted Beta-Liouville has a more general covariance structure and a smaller number of parameters than the inverted Dirichlet and generalized inverted Dirichlet, respectively, which makes it more practical and useful. A principled Bayesian learning algorithm is developed to accurately estimate the model’s parameters. To cope with the problem of selecting the optimal number of components, we further propose a nonparametric Bayesian learning algorithm based on an extended infinite mixture model which may have better modelling and clustering capabilities than the finite model for some applications. Finally, the resulting generative model is exploited to build several efficient probabilistic SVM kernels in order to enhance the expected clustering and modeling performance. Through a number of experimental evaluations involving visual scenes classification, text categorization and texture images discrimination, we prove the merits of the proposed work.

Highlights

  • With the proliferation of new technologies, millions of people generate large heterogeneous data, through smart devices, which represent an excellent opportunity to enhance knowledge in broad areas, including data science, statistical data analysis, and other business problems

  • Some recent works have demonstrated that inverted Dirichlet (ID) and generalized inverted Dirichlet (GID) distributions are better solutions than conventional Gaussian for modeling and clustering positive data vectors [11]

  • This paper focuses on increasing the classification performance by introducing a new hybrid learning approach that takes into account the benefits of both discriminative SVM kernels and generative IBLMM mixture

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Summary

INTRODUCTION

With the proliferation of new technologies, millions of people generate large heterogeneous data, through smart devices, which represent an excellent opportunity to enhance knowledge in broad areas, including data science, statistical data analysis, and other business problems. The challenge is to find the most powerful distribution, as well as the best inference method for learning mixture models in order to model effectively positive data vectors (i.e., vectors greater than 0) and perform accurate classification. Some recent works have demonstrated that inverted Dirichlet (ID) and generalized inverted Dirichlet (GID) distributions are better solutions than conventional Gaussian for modeling and clustering positive data vectors [11] These distributions present some drawbacks that limit their use in several real problems. FINITE INVERTED BETA-LIOUVILLE MIXTURE MODEL We start this section by presenting the Liouville family of distributions and the inverted Beta-Liouville distribution, we propose a finite mixture based on the inverted Beta-Liouville that we denote by IBL mixtures

THE INVERTED BETA-LIOUVILLE DISTRIBUTION
PRIORS AND POSTERIORS
INFORMATION DIVERGENCE KERNELS
EXPERIMENTAL RESULTS
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