TY - GEN
T1 - A method to estimate the true mahalanobis distance from eigenvectors of sample covariance matrix
AU - Iwamura, Masakazu
AU - Omachi, Shinichiro
AU - Aso, Hirotomo
N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2002.
PY - 2002
Y1 - 2002
N2 - In statistical pattern recognition, the parameters of distributions are usually estimated from training sample vectors. However, estimated parameters contain estimation errors, and the errors cause bad influence on recognition performance when the sample size is not sufficient. Some methods can obtain better estimates of the eigenvalues of the true covariance matrix and can avoid bad influences caused by estimation errors of eigenvalues. However, estimation errors of eigenvectors of covariance matrix have not been considered enough. In this paper, we consider estimation errors of eigenvectors and show the errors can be regarded as estimation errors of eigenvalues. Then, we present a method to estimate the true Mahalanobis distance from eigenvectors of the sample covariance matrix. Recognition experiments show that by applying the proposed method, the true Mahalanobis distance can be estimated even if the sample size is small, and better recognition accuracy is achieved. The proposed method is useful for the practical applications of pattern recognition since the proposed method is effective without any hyper-parameters.
AB - In statistical pattern recognition, the parameters of distributions are usually estimated from training sample vectors. However, estimated parameters contain estimation errors, and the errors cause bad influence on recognition performance when the sample size is not sufficient. Some methods can obtain better estimates of the eigenvalues of the true covariance matrix and can avoid bad influences caused by estimation errors of eigenvalues. However, estimation errors of eigenvectors of covariance matrix have not been considered enough. In this paper, we consider estimation errors of eigenvectors and show the errors can be regarded as estimation errors of eigenvalues. Then, we present a method to estimate the true Mahalanobis distance from eigenvectors of the sample covariance matrix. Recognition experiments show that by applying the proposed method, the true Mahalanobis distance can be estimated even if the sample size is small, and better recognition accuracy is achieved. The proposed method is useful for the practical applications of pattern recognition since the proposed method is effective without any hyper-parameters.
UR - http://www.scopus.com/inward/record.url?scp=23044532375&partnerID=8YFLogxK
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U2 - 10.1007/3-540-70659-3_52
DO - 10.1007/3-540-70659-3_52
M3 - Conference contribution
AN - SCOPUS:23044532375
SN - 3540440119
SN - 9783540440116
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 498
EP - 507
BT - Structural, Syntactic, and Statistical Pattern Recognition - Joint IAPR International Workshops SSPR 2002 and SPR 2002, Proceedings
A2 - Caelli, Terry
A2 - Amin, Adnan
A2 - Duin, Robert P.W.
A2 - de Ridder, Dick
A2 - Kamel, Mohamed
PB - Springer Verlag
T2 - Joint IAPR 9th International Workshop on Structural and Syntactic Pattern Recognition, SSPR 2002 and 4th International Workshop on Statistical Techniques in Pattern Recognition, SPR 2002
Y2 - 6 August 2002 through 9 August 2002
ER -