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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)
|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 -58)
|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.|
|Online Catalog Link: ||http://lib.cityu.edu.hk/record=b2374934|
|Appears in Collections:||MA - Doctor of Philosophy |
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