Kernel Discriminant Analysis based on Generalized Singular Value Decomposition
نویسندگان
چکیده
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.
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Nonlinear Discriminant Analysis Using Kernel Functions and the Generalized Singular Value Decomposition
Linear Discriminant Analysis (LDA) has been widely used for linear dimension reduction. However, LDA has some limitations that one of the scatter matrices is required to be nonsingular and the nonlinearly clustered structure is not easily captured. In order to overcome the problems caused by the singularity of the scatter matrices, a generalization of LDA based on the generalized singular value...
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