Weighted generalized kernel discriminant analysis using fuzzy memberships

Authors:
Jing Yang;Liya Fan
Affiliations:
Liaocheng University, School of Mathematics Sciences, Liaocheng, P.R. China;Liaocheng University, School of Mathematics Sciences, Liaocheng, P.R. China
Venue:
WSEAS Transactions on Mathematics
Year:
2011

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Abstract

Linear discriminant analysis (LDA) is a classical approach for dimensionality reduction. However, LDA has limitations in that one of the scatter matrices is required to be nonsingular and the nonlinearly clustered structure is not easily captured. In order to overcome these problems, in this paper, we present several generalizations of kernel fuzzy discriminant analysis (KFDA) which include KFDA based on generalized singular value decomposition (KFDA/GSVD), pseudo-inverse KFDA (PIKFDA) and range space KFDA (RSKFDA). These KFDA-based algorithms adopts kernel methods to accommodate nonlinearly separable cases. In order to remedy the problem that KFDA-based algorithms fail to consider that different contribution of each pair of class to the discrimination, weighted schemes are incorporated into KFDA extensions in this paper and called them weighted generalized KF-DA algorithms. Experiments on three real-world data sets are performed to test and evaluate the effectiveness of the proposed algorithms and the effect of weights on classification accuracy. The results show that the effect of weighted schemes is very significantly.