Visual Analysis of the Use of Mixture Covariance Matrices in Face Recognition

Abstract

The quadratic discriminant (QD) classifier has proved to be simple and effective in many pattern recognition problems. However, it requires the computation of the inverse of the sample group covariance matrix. In many biometric problems, such as face recognition, the number of training patterns is considerably smaller than the number of features, and therefore the covariance matrix is singular. Several studies have shown that the use of mixture covariance matrices defined as a combination between the sample group covariance matrices and, for instance, the pooled covariance matrix, not only overcomes the singularity and instability of the sample group covariance matrices but also improves the QD classifier performance. However, little attention has been paid to understanding what has happened with the final shape of these mixture covariance matrices. In this work, we visually analyse in the commonly used eigenfaces space the eigenvectors and eigenvalues of these covariance matrices, given by the three following approaches: maximum likelihood, maximum classification accuracy, and maximum entropy. Experiments using the two well-known ORL and FERET face databases have shown that the maximum entropy approach is the one that achieves a more intuitive visual performance and best classification accuracies, especially in face experiments where moderate changes in facial expressions, pose, and scale, occur.