A Novel Bayesian Logistic Discriminant Model with Dirichlet Distributions: An Application to Face Recognition

Abstract

The Linear Discriminant Analysis (LDA) is a linear classifier which has proven to be powerful and competitive compared to the main state-of-the-art classifiers. However, the LDA assumes that the class conditional distributions are symmetric Gaussians with identical covariance structures, assumptions that are untrue for many classification and pattern recognition applications using heteroscedastic and asymmetric data. In this paper, a novel Bayesian Logistic Discriminant model with Dirichlet distributions (BLDD) is proposed to further relax the assumptions of the LDA by representing each class by a different Dirichlet distribution. At the same time, the BLDD tackles the so-called small sample size problem using a sparsity-promoting Gaussian prior over the unknown parameters. An extensive comparison of the BLDD to both LDA and Support Vector Machine (SVM) classifiers, performed on artificial and real datasets, has shown the advantages and superiority of our proposed method. In particular, the experiments on face recognition have clearly shown a significant improvement of the BLDD over the LDA.