BibTeX
@MISC{Park_generalizedsingular,
author = {Cheonghee Park and Haesun Park},
title = {Generalized Singular Value Decomposition},
year = {}
}
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Abstract
In Linear Discriminant Analysis (LDA), a dimension reducing linear transformation is found in order to better distinguish clusters from each other in the reduced dimensional space. However, LDA has a limitation that one of the scatter matrices is required to be nonsingular and the nonlinearly clustered structure is not easily captured. We propose a nonlinear discriminant analysis based on kernel functions and the generalized singular value decomposition called KDA/GSVD, which is a nonlinear extension of LDA and works regardless of the nonsingularity of the scatter matrices in either the input space or feature space. Our experimental results show that our method is a very effective nonlinear dimension reduction method.
Keyphrases
singular value decomposition scatter matrix distinguish cluster nonlinear discriminant analysis reduced dimensional space feature space kernel function generalized singular value decomposition linear discriminant analysis input space clustered structure kda gsvd linear transformation experimental result effective nonlinear dimension reduction method nonlinear extension
