TY - JOUR

T1 - Estimation of true Mahalanobis distance from eigenvectors of sample covariance matrix

AU - Iwamura, Masakazu

AU - Omachi, Shinichiro

AU - Aso, Hirotomo

PY - 2004/8

Y1 - 2004/8

N2 - 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.

AB - 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.

KW - Discriminant function

KW - Eigenvector

KW - Estimation error

KW - Mahalanobis distance

KW - Pattern recognition

UR - http://www.scopus.com/inward/record.url?scp=4444360488&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=4444360488&partnerID=8YFLogxK

U2 - 10.1002/scj.10519

DO - 10.1002/scj.10519

M3 - Article

AN - SCOPUS:4444360488

SN - 0882-1666

VL - 35

SP - 30

EP - 38

JO - Systems and Computers in Japan

JF - Systems and Computers in Japan

IS - 9

ER -