Title:
Relationships Between Support Vector Classifiers and Generalized Linear Discriminant Analysis on Support Vectors
Relationships Between Support Vector Classifiers and Generalized Linear Discriminant Analysis on Support Vectors
Author(s)
Kim, Hyunsoo
Drake, Barry L.
Park, Haesun
Drake, Barry L.
Park, Haesun
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Abstract
The linear discriminant analysis based on the generalized singular value decomposition
(LDA/GSVD) has been introduced to circumvent the nonsingularity restriction inherent in
the classical LDA. The LDA/GSVD provides a framework in which a dimension reducing transformation
can be effectively obtained for undersampled problems. In this paper, relationships between
support vector machines (SVMs) and the generalized linear discriminant analysis applied
to the support vectors are studied. Based on the GSVD, the weight vector of the hard-margin
SVM is proved to be equivalent to the dimension reducing transformation vector generated by
LDA/GSVD applied to the support vectors of the binary class. We also show that the dimension
reducing transformation vector and the weight vector of soft-margin SVMs are related when a
subset of support vectors are considered. These results can be generalized when kernelized SVMs
and the kernelized LDA/GSVD called KDA/GSVD are considered. Through these relationships,
it is shown that support vector classification is related to data reduction as well as dimension
reduction by LDA/GSVD.
Sponsor
This material is based upon work supported in part by the National Science Foundation Grants CCR-0204109
and ACI-0305543. Any opinions, findings and conclusions or recommendations expressed in this material are those
of the authors and do not necessarily reflect the views of the National Science Foundation.
Date Issued
2006
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Text
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Technical Report