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Activity Number: 295
Type: Contributed
Date/Time: Tuesday, July 31, 2012 : 8:30 AM to 10:20 AM
Sponsor: Section on Statistical Learning and Data Mining
Abstract - #306687
Title: Demystifying Feature Mapping via Kernels
Author(s): Zhiyu Liang*+ and Yoonkyung Lee
Companies: The Ohio State University and The Ohio State University
Address: 231 Cockins Hall, 1958 Neil Avenue, Columbus, OH, 43210, United States

There has been growing interest in kernel methods for classification, clustering and dimension reduction. For example, kernel linear discriminant analysis (KLDA), spectral clustering and kernel principal component analysis (KPCA) are widely used in statistical learning and data mining applications. The empirical success of the kernel method is generally attributed to nonlinear feature mapping induced by the kernel, which in turn determines a low dimensional data embedding. However, there is lack of understanding of the effect of a kernel and its associated kernel parameter(s) on the embedding in relation to data distributions. By coupling data distributions with different kernels, we examine the geometry of the nonlinear embedding induced by kernels. We also investigate the effect of kernel parameters. The results provide both insights into the geometry of nonlinear data embedding and practical guidelines for choosing appropriate parameters for kernel methods.

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