Support Vector Machine algorithms : analysis and applications
Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2002.
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| Format: | Thesis |
| Language: | eng |
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Massachusetts Institute of Technology
2005
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| Online Access: | http://hdl.handle.net/1721.1/8404 |
| _version_ | 1826208873411772416 |
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| author | Wen, Tong, 1970- |
| author2 | Alan Edelman. |
| author_facet | Alan Edelman. Wen, Tong, 1970- |
| author_sort | Wen, Tong, 1970- |
| collection | MIT |
| description | Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2002. |
| first_indexed | 2024-09-23T14:13:59Z |
| format | Thesis |
| id | mit-1721.1/8404 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T14:13:59Z |
| publishDate | 2005 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/84042019-04-11T06:06:49Z Support Vector Machine algorithms : analysis and applications SVM algorithms : analysis and applications Wen, Tong, 1970- Alan Edelman. Massachusetts Institute of Technology. Dept. of Mathematics. Massachusetts Institute of Technology. Dept. of Mathematics. Mathematics. Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2002. Includes bibliographical references (p. 89-97). Support Vector Machines (SVMs) have attracted recent attention as a learning technique to attack classification problems. The goal of my thesis work is to improve computational algorithms as well as the mathematical understanding of SVMs, so that they can be easily applied to real problems. SVMs solve classification problems by learning from training examples. From the geometry, it is easy to formulate the finding of SVM classifiers as a linearly constrained Quadratic Programming (QP) problem. However, in practice its dual problem is actually computed. An important property of the dual QP problem is that its solution is sparse. The training examples that determine the SVM classifier are known as support vectors (SVs). Motivated by the geometric derivation of the primal QP problem, we investigate how the dual problem is related to the geometry of SVs. This investigation leads to a geometric interpretation of the scaling property of SVMs and an algorithm to further compress the SVs. A random model for the training examples connects the Hessian matrix of the dual QP problem to Wishart matrices. After deriving the distributions of the elements of the inverse Wishart matrix Wn-1(n, nI), we give a conjecture about the summation of the elements of Wn-1(n, nI). It becomes challenging to solve the dual QP problem when the training set is large. We develop a fast algorithm for solving this problem. Numerical experiments show that the MATLAB implementation of this projected Conjugate Gradient algorithm is competitive with benchmark C/C++ codes such as SVMlight and SvmFu. Furthermore, we apply SVMs to time series data. (cont.) In this application, SVMs are used to predict the movement of the stock market. Our results show that using SVMs has the potential to outperform the solution based on the most widely used geometric Brownian motion model of stock prices. by Tong Wen. Ph.D. 2005-08-23T19:55:30Z 2005-08-23T19:55:30Z 2002 2002 Thesis http://hdl.handle.net/1721.1/8404 50600599 eng M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582 97 p. 6704574 bytes 6704331 bytes application/pdf application/pdf application/pdf Massachusetts Institute of Technology |
| spellingShingle | Mathematics. Wen, Tong, 1970- Support Vector Machine algorithms : analysis and applications |
| title | Support Vector Machine algorithms : analysis and applications |
| title_full | Support Vector Machine algorithms : analysis and applications |
| title_fullStr | Support Vector Machine algorithms : analysis and applications |
| title_full_unstemmed | Support Vector Machine algorithms : analysis and applications |
| title_short | Support Vector Machine algorithms : analysis and applications |
| title_sort | support vector machine algorithms analysis and applications |
| topic | Mathematics. |
| url | http://hdl.handle.net/1721.1/8404 |
| work_keys_str_mv | AT wentong1970 supportvectormachinealgorithmsanalysisandapplications AT wentong1970 svmalgorithmsanalysisandapplications |