TY - GEN
T1 - Non-iterative heteroscedastic linear dimension reduction for two-class data; from Fisher to Chernoff
AU - Loog, M
AU - Duin, RPW
N1 - ISSN 0302-9743, phpub 29
PY - 2002
Y1 - 2002
N2 - Linear discriminant analysis (LDA) is a traditional solution to the linear dimension reduction (LDR) problem, which is based on the maximization of the between-class scatter over the within-class scatter. This solution is incapable of dealing with heteroscedastic data in a proper way, because of the implicit assumption that the covariance matrices for all the classes are equal. Hence, discriminatory information in the difference between the covariance matrices is not used and, as a consequence, we can only reduce the data to a single dimension in the two-class case.
We propose a fast non-iterative eigenvector-based LDR technique for heteroscedastic two-class data, which generalizes, and improves upon LDA by dealing with the aforementioned problem. For this purpose, we use the concept of directed distance matrices, which generalizes the between-class covariance matrix such that it captures the differences in (co)variances.
AB - Linear discriminant analysis (LDA) is a traditional solution to the linear dimension reduction (LDR) problem, which is based on the maximization of the between-class scatter over the within-class scatter. This solution is incapable of dealing with heteroscedastic data in a proper way, because of the implicit assumption that the covariance matrices for all the classes are equal. Hence, discriminatory information in the difference between the covariance matrices is not used and, as a consequence, we can only reduce the data to a single dimension in the two-class case.
We propose a fast non-iterative eigenvector-based LDR technique for heteroscedastic two-class data, which generalizes, and improves upon LDA by dealing with the aforementioned problem. For this purpose, we use the concept of directed distance matrices, which generalizes the between-class covariance matrix such that it captures the differences in (co)variances.
KW - conference contrib. refereed
KW - ZX CWTS JFIS < 1.00
UR - http://link.springer.de/link/service/series/0558/bibs/2396/23960508.htm
M3 - Conference contribution
SN - 3-540-44011-9
SP - 488
EP - 496
BT - Structural, Syntactic, and Statistical Pattern Recognition, Proceedings
A2 - Caelli, T
A2 - Amin, A
A2 - Duin, RPW
A2 - Kamel, M
A2 - de Ridder, D
PB - Springer
CY - Berlin
T2 - Joint IAPR International Workshops SSPR'02 and SPR'02 (Windsor, Canada)
Y2 - 6 August 2002 through 9 August 2002
ER -