A division algebraic framework for multidimensional support vector regression

Authors:
Alistair Shilton;Daniel T. H. Lai;Marimuthu Palaniswami
Affiliations:
Department of Electrical and Electronic Engineering, The University of Melbourne, Melbourne, Vic., Australia;Centre for Ageing, Rehabilitation, Exercise and Sport, Victoria University, Melbourne, Vic., Australia;Department of Electrical and Electronic Engineering, The University of Melbourne, Melbourne, Vic., Australia
Venue:
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Year:
2010

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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 εX-SVR is proposed based on an ε-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 ε-SVR. The εH-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 εH-SVR performs significantly better than the C-SVR, the LS-SVR, and theM-SVR in terms ofmean-squared error, outlier sensitivity, and support vector sparsity.