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 ? Z -SVR is proposed based on an ?-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 ?-SVR. The ? 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 ? 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.
['Alistair Shilton', 'Daniel T. H. Lai', 'Marimuthu Palaniswami']
A Division Algebraic Framework for Multidimensional Support Vector Regression