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Speed Up Kernel Discriminant Analysis

By Deng Cai, Xiaofei He and Jiawei Han


Linear Discriminant Analysis (LDA) has been a popular method for dimensionality reduction which preserves 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 eigendecomposition 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, SRKDAcastsdiscriminantanalysisinto 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. The new formulation makes it very easy to develop incremental version of the algorithm which ca

Year: 2011
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