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A division algebraic framework for multidimensional support vector regression
journal contribution
posted on 2010-04-01, 00:00 authored by Alistair ShiltonAlistair Shilton, D T H Lai, M PalaniswamiIn 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 the M-SVR in terms of mean-squared error, outlier sensitivity, and support vector sparsity.
History
Journal
IEEE transactions on systems, man, and cybernetics, part B: cyberneticsVolume
40Issue
2Pagination
517 - 528Publisher
Institute of Electrical and Electronics EngineersLocation
Piscataway, N.J.Publisher DOI
ISSN
1083-4419Language
engPublication classification
C1.1 Refereed article in a scholarly journalCopyright notice
2009, IEEEUsage metrics
Keywords
Clifford algebracomplex numbersdivision algebramultidimensional regressionmultiple input–multiple output (MIMO)quaternionssupport vector regression (SVR)Science & TechnologyTechnologyAutomation & Control SystemsComputer Science, Artificial IntelligenceComputer Science, CyberneticsComputer Sciencemultiple input-multiple output (MIMO)EQUALIZATIONNETWORKSArtificial Intelligence and Image Processing
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