Estimation of True Mahalanobis Distance from Eigenvectors of Sample Covariance Matrix

要約

In statistical pattern recognition, the Bayesian decision theory gives a decision to minimize the expected probability of misclassification as long as the true distributions are given. However, in most practical situations, the true distributions are unknown, and the parameters of the distributions are usually estimated from training sample vectors. It is well-known that estimated parameters contain estimation errors when sample size is small, and the errors cause bad influence on recognition performance. Among the estimation errors of parameters, the estimation errors of eigenvectors have not been considered enough. In this paper, we present a method to estimate the true Mahalanobis distance from the sample eigenvectors (the eigenvectors of sample covariance matrix) by considering the estimation errors of eigenvectors. Recognition experiments show that the true Mahalanobis distance can be estimated, and better recognition accuracy is achieved by applying the proposed method without many training samples and any hyper-parameters.

注記