Separate-Group Covariance Estimation With Insufficient Data for Object Recognition

Many similarity measures used for classification involve the inverse of the group covariance matrices. However, the number of observations available in the training set for each group is, in many cases, significantly inferior to the dimension of the feature space, what implies that the sample covariance matrix is singular. A common solution to this problem is to assume the same covariance matrix for all groups using the pooled covariance matrix computed from the whole training set. This paper investigates an alternative estimate for the group covariance matrices, called Mixed Covariance, given by a linear combination of the sample group and pooled covariance matrices. This estimate has the same rank of the pooled covariance matrix without assuming equal covariance for all groups. Experiments were carried out to evaluate the performance associated with the proposed estimate in two automatic recognition applications: face and facial expression. The average recognition rates obtained by using the mixed covariance were higher than the usual sample group and pooled covariance estimates.