Using Mixture Covariance Matrices to Improve Face and Facial Expression Recognitions

In several pattern recognition problems, particularly in image recognition ones, there are often a large number of features available, but the number of training samples for each pattern is significantly less than the dimension of the feature space. This statement implies that the sample group covariance matrices often used in the Gaussian maximum probability classifier are singular. A common solution to this problem is to assume that all groups have equal covariance matrices and to use as their estimates the pooled covariance matrix calculated from the whole training set. This paper uses an alternative estimate for the sample group covariance matrices, here called the mixture covariance, given by an appropriate linear combination of the sample group and pooled covariance matrices. Experiments were carried out to evaluate the performance associated with this estimate in two recognition applications: face and facial expression. The average recognition rates obtained by using the mixture covariance matrices were higher than the usual estimates.