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A Note on Octonionic Support Vector Regression

Authors
Publisher
IEEE
Publication Date
Keywords
  • 0802 Computation Theory And Mathematics
  • 0903 Biomedical Engineering
  • School Of Sport And Exercise Science
  • 9202 Health And Support Services
  • School Of Engineering And Science
Disciplines
  • Mathematics

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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