Demystifying Feature Mapping via Kernels

• 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
• Author(s): Zhiyu Liang*+ and Yoonkyung Lee
• Companies: The Ohio State University and The Ohio State University

Abstract

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.