Covariance estimation in full- and reduced-dimensionality image classification
Image and Vision Computing
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In statistical pattern recognition, the Bayesian decision theory gives a decision that minimizes 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 the sample size is small, and the errors have a negative influence on recognition performance. Among the estimation errors of parameters, the estimation errors of eigenvectors have not been sufficiently considered. 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 hyperparameters. © 2004 Wiley Periodicals, Inc. Syst Comp Jpn, 35(9): 30–38, 2004; Published online in Wiley InterScience (). DOI 10.1002/scj.10519