title: A division algebraic framework for multidimensional support vector regression.
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 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.
authors.affiliation: Department of Electrical and Electronic Engineering, The University of Melbourne, Melbourne, Vic. 3010, Australia. apsh@ee.unimelb.edu.au
authors.forename: Alistair
authors.initials: A
authors.lastname: Shilton
authors.forename: Daniel T H
authors.initials: DT
authors.lastname: Lai
authors.forename: Marimuthu
authors.initials: M
authors.lastname: Palaniswami