Journal article

A Division Algebraic Framework for Multidimensional Support Vector Regression

Alistair Shilton, Daniel TH Lai, Marimuthu Palaniswami

IEEE TRANSACTIONS ON SYSTEMS MAN AND CYBERNETICS PART B-CYBERNETICS | IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC | Published : 2010

Abstract

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..

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Funding Acknowledgements

Manuscript received October 3, 2008; revised February 19, 2009 and May 29, 2009. First published September 4, 2009; current version published March 17, 2010. This work was supported in part by Department of Education, Science and Training (DEST) International Science Linkages (ISL) and in part by the Australian Research Council. This paper was recommended by Associate Editor Z. R. Yang.