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Title: Dimensionality reduction by kernel CCA in reproducing kernel hilbert spaces
Keywords: Dimensionality Reduction, Kernel Canonical Correlation Analysis, Reproducing Kernel Hilbert Spaces, Principal Component Analysis, Kernel Methods,
Issue Date: 1-Jul-2009
Citation: ZHU XIAOFENG (2009-07-01). Dimensionality reduction by kernel CCA in reproducing kernel hilbert spaces. ScholarBank@NUS Repository.
Abstract: In the thesis, we employ a multi-modal method (i.e., kernel canonical correlation analysis) named RKCCA to implement dimensionality reduction for high dimensional data. Our RKCCA method first maps the original data into the Reproducing Kernel Hilbert Space (RKHS) by explicit kernel functions, whereas the traditional KCCA (referred to as spectrum KCCA) method projects the input into high dimensional Hilbert space by implicit kernel functions. This makes the RKCCA method more suitable for theoretical development. Furthermore, we prove the equivalence between our RKCCA and spectrum KCCA. In RKHS, we prove that RKCCA method can be decomposed into two separate steps, i.e., principal component analysis (PCA) followed by canonical correlation analysis (CCA). We also prove that the rule can be preserved for implementing dimensionality reduction in RKHS. Experimental results on real-world datasets show the presented method yields better performance than the sate-of-the-art algorithms in terms of classification accuracy and the effect of dimensionality reduction.
Appears in Collections:Master's Theses (Open)

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