A Division Algebraic Framework for Multidimensional Support Vector Regression

作者：Shilton Alistair^*; Lai Daniel T H; Palaniswami Marimuthu

来源：IEEE Transactions on Systems, Man, and Cybernetics - Part B: Cybernetics , 2010, 40(2): 517-528.

DOI：10.1109/TSMCB.2009.2028314

• Clifford algebra
• complex numbers
• division algebra
• multidimensional regression
• multiple input-multiple output (MIMO)
• quaternions
• support vector regression (SVR)

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(X)-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.

• 出版日期2010-4