Robust Estimation of Distribution by Shrinkage Technique

Most pattern recognition applications require the eigenvalues and eigenvectors of the covariance matrix. It is well known that when the number of training samples is small, the eigenvalues of the covariance matrix contains bias, and the bias degrades recognition performance. There are some methods which ignore the small eigenvalues, or acquire better estimates of the covariance matrix by correcting the eigenvalues. Though all of these methods cope with the eigenvalues obtained after eigen decomposition, eigen decomposition seems to cause the biases of the eigenvalues. Therefore, it is worth trying to devise a method which avoids bias of eigenvalues. In this paper, it is confirmed that biases of the eigenvalues appear after eigen decomposition by experiments. Then a method of shrinking the covariance matrix before eigen decomposition for avoiding bias of the eigenvalues are proposed. The ability of the proposed method of estimating the true distribution more precisely than using the sample covariance matrix and of improving recognition performance is confirmed by the recognition experiments.