A Division Algebraic Framework for Multidimensional Support Vector Regression
AuthorShilton, A; Lai, DTH; Palaniswami, M
Source TitleIEEE TRANSACTIONS ON SYSTEMS MAN AND CYBERNETICS PART B-CYBERNETICS
PublisherIEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
AffiliationElectrical And Electronic Engineering
Document TypeJournal Article
CitationsShilton, A; Lai, DTH; Palaniswami, M, A Division Algebraic Framework for Multidimensional Support Vector Regression, IEEE TRANSACTIONS ON SYSTEMS MAN AND CYBERNETICS PART B-CYBERNETICS, 2010, 40 (2), pp. 517 - 528
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C1 - Journal Articles Refereed
In this paper, division algebras are proposed as an elegant basis upon which to extend support vector regression (SVR) to multidimensional targets. Using this framework, a multitarget SVR called epsilon(Z)-SVR is proposed based on an epsilon-insensitive loss function that is independent of the coordinate system or basis used. This is developed to dual form in a manner that is analogous to the standard epsilon-SVR. The epsilon(H)-SVR is compared and contrasted with the least-square SVR (LS-SVR), the Clifford SVR (C-SVR), and the multidimensional SVR (M-SVR). Three practical applications are considered: namely, 1) approximation of a complex-valued function; 2) chaotic time-series prediction in 3-D; and 3) communication channel equalization. Results show that the epsilon(H)-SVR performs significantly better than the C-SVR, the LS-SVR, and the M-SVR in terms of mean-squared error, outlier sensitivity, and support vector sparsity.
KeywordsElectrical and Electronic Engineering not elsewhere classified; Expanding Knowledge in Engineering
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