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Efficient Kernel Discriminant Analysis via Spectral Regression

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Title: Efficient Kernel Discriminant Analysis via Spectral Regression
Author(s): Cai, Deng; He, Xiaofei; Han, Jiawei
Subject(s): algorithms
Abstract: Linear Discriminant Analysis (LDA) has been a popular method for extracting features which preserve class separability. The projection vectors are commonly obtained by maximizing the between class covariance and simultaneously minimizing the within class covariance. LDA can be performed either in the original input space or in the reproducing kernel Hilbert space (RKHS) into which data points are mapped, which leads to Kernel Discriminant Analysis (KDA). When the data are highly nonlinear distributed, KDA can achieve better performance than LDA. However, computing the projective functions in KDA involves eigen-decomposition of kernel matrix, which is very expensive when a large number of training samples exist. In this paper, we present a new algorithm for kernel discriminant analysis, called Spectral Regression Kernel Discriminant Analysis (SRKDA). By using spectral graph analysis, SRKDA casts discriminant analysis into a regression framework which facilitates both efficient computation and the use of regularization techniques. Specifically, SRKDA only needs to solve a set of regularized regression problems and there is no eigenvector computation involved, which is a huge save of computational cost. Moreover, the new formulation makes it very easy to develop incremental version of the algorithm which can fully utilize the computational results of the existing training samples. Extensive experiments on spoken letter, handwritten digit image and face image data demonstrate the effectiveness and efficiency of the proposed algorithm.
Issue Date: 2007-08
Genre: Technical Report
Type: Text
URI: http://hdl.handle.net/2142/11377
Other Identifier(s): UIUCDCS-R-2007-2888
Rights Information: You are granted permission for the non-commercial reproduction, distribution, display, and performance of this technical report in any format, BUT this permission is only for a period of 45 (forty-five) days from the most recent time that you verified that this technical report is still available from the University of Illinois at Urbana-Champaign Computer Science Department under terms that include this permission. All other rights are reserved by the author(s).
Date Available in IDEALS: 2009-04-22
 

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