Skip to Main Content
 

Global Search Box

 
 
 
 

Files

File List


dissertation.pdf (1.04 MB)

ETD Abstract Container

Abstract Header

Eigen-analysis of kernel operators for nonlinear dimension reduction and discrimination

Liang, Zhiyu
http://rave.ohiolink.edu/etdc/view?acc_num=osu1388676476

Abstract Details

2014, Doctor of Philosophy, Ohio State University, Statistics.
There has been growing interest in kernel methods for classification, clustering and dimension reduction. For example, kernel linear discriminant analysis, spectral clustering and kernel principal component analysis 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. It is important to understand the eff ect of a kernel and its associated kernel parameter(s) on the embedding in relation to data distributions. In this dissertation, we examine the geometry of the nonlinear embeddings for kernel PCA and kernel LDA through spectral analysis of the corresponding kernel operators. In particular, we carry out eigen-analysis of the polynomial kernel operator associated with data distributions and investigate the eff ect of the degree of polynomial on the data embedding. We also investigate the eff ect of centering kernels on the spectral property of both polynomial and Gaussian kernel operators. In addition, we extend the framework of the eigen-analysis of kernel PCA to kernel LDA by considering between-class and within-class variation operators for polynomial kernels. The results provide both insights into the geometry of nonlinear data embeddings given by kernel methods and practical guidelines for choosing an appropriate degree for dimension reduction and discrimination with polynomial kernels.
Yoonkyung Lee (Advisor)
Tao Shi (Committee Member)
Vincent Vu (Committee Member)
128 p.
Statistics
centering, Gaussian kernel, kernel LDA, kernel methods, kernel PCA, nonlinear embedding, polynomial kernel

Recommended Citations

Citations

  • Liang, Z. (2014). Eigen-analysis of kernel operators for nonlinear dimension reduction and discrimination [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1388676476

    APA Style (7th edition)

  • Liang, Zhiyu. Eigen-analysis of kernel operators for nonlinear dimension reduction and discrimination. 2014. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1388676476.

    MLA Style (8th edition)

  • Liang, Zhiyu. "Eigen-analysis of kernel operators for nonlinear dimension reduction and discrimination." Doctoral dissertation, Ohio State University, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=osu1388676476

    Chicago Manual of Style (17th edition)

osu1388676476
4,473
© 2014, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.