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Title: Learning gradients and canonical correlation by kernel methods
Other Titles: Tong guo he fang fa xue xi ti du he dian xing xiang guan
Authors: Cai, Jia (蔡佳)
Department: Department of Mathematics
Degree: Doctor of Philosophy
Issue Date: 2009
Publisher: City University of Hong Kong
Subjects: Conjugate gradient methods
Canonical correlation (Statistics)
Kernel functions.
Notes: CityU Call Number: QA218 .C34 2009
iv, 58 leaves 30 cm.
Thesis (Ph.D.)--City University of Hong Kong, 2009.
Includes bibliographical references (leaves [52]-58)
Type: thesis
Abstract: In this thesis, we focus on gradient learning and canonical correlation analysis (CCA) by kernel methods. The motivations are to select important features when large amount of data with high dimensions are available. Detailed error analysis of some learning algorithm for gradient learning and kernel CCA are provided. We first review the topic of gradient learning, both for regression problems and classification problems. In a classification setting involving a convex loss function, a possible algorithm for gradient learning is implemented by solving convex quadratic programming optimization problems induced by regularization schemes in reproducing kernel Hilbert spaces. The complexity for such an algorithm might be very high when the number of variables or samples is huge. To reduce the complexity, a gradient descent algorithm for gradient learning in a classification setting is proposed. The implementation of the algorithm is simple. Explicit learning rates are presented in terms of the regularization parameter and the step size. Deep analysis for approximation by reproducing kernel Hilbert spaces under some mild conditions on the probability measure for sampling allows us to deal with a general class of convex loss functions. We then consider the CCA problem and a nonlinear extension, kernel canonical correlation analysis. Detailed convergence analysis is conducted by means of properties of related functions and kernels. Our analysis gives better understanding of CCA.
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