A Note on Octonionic Support Vector Regression

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Shilton, A, Lai, Daniel ORCID: 0000-0003-3459-7709, Santhiranayagam, Braveena K and Palaniswami, M (2012) A Note on Octonionic Support Vector Regression. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, 42 (3). pp. 950-955. ISSN 1083-4419 (print) 1941-0492 (online)

Abstract

This note presents an analysis of the octonionic form of the division algebraic support vector regressor (SVR) first introduced by Shilton A detailed derivation of the dual form is given, and three conditions under which it is analogous to the quaternionic case are exhibited. It is shown that, in the general case of an octonionic-valued feature map, the usual “kernel trick” breaks down. The cause of this (and its interpretation) is discussed in some detail, along with potential ways of extending kernel methods to take advantage of the distinct features present in the general case. Finally, the octonionic SVR is applied to an example gait analysis problem, and its performance is compared to that of the least squares SVR, the Clifford SVR, and the multidimensional SVR.

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Item type Article
URI https://vuir.vu.edu.au/id/eprint/7634
DOI https://doi.org/10.1109/TSMCB.2011.2170564
Official URL http://dx.doi.org/10.1109/TSMCB.2011.2170564
Subjects Current > FOR Classification > 0802 Computation Theory and Mathematics
Current > FOR Classification > 0903 Biomedical Engineering
Historical > Faculty/School/Research Centre/Department > School of Sport and Exercise Science
Historical > SEO Classification > 9202 Health and Support Services
Historical > Faculty/School/Research Centre/Department > School of Engineering and Science
Keywords ResPubID22857, ResPubID25398, Clifford algebra, complex numbers, division algebra, gait analysis, multidimensional regression, multiple-output (MIMO), octonions, quaternions, support vector regressor (SVR)
Citations in Scopus 4 - View on Scopus
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