
pmid: 22106150
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.
ResPubID22857, 9202 Health and Support Services, ResPubID25398, Decision Support Techniques, Pattern Recognition, Automated, 0903 Biomedical Engineering, division algebra, Artificial Intelligence, School of Engineering and Science, complex numbers, Computer Simulation, Clifford algebra, 0802 Computation Theory and Mathematics, quaternions, Models, Statistical, support vector regressor (SVR), multidimensional regression, School of Sport and Exercise Science, multiple-output (MIMO), 620, octonions, gait analysis, Regression Analysis, Algorithms
ResPubID22857, 9202 Health and Support Services, ResPubID25398, Decision Support Techniques, Pattern Recognition, Automated, 0903 Biomedical Engineering, division algebra, Artificial Intelligence, School of Engineering and Science, complex numbers, Computer Simulation, Clifford algebra, 0802 Computation Theory and Mathematics, quaternions, Models, Statistical, support vector regressor (SVR), multidimensional regression, School of Sport and Exercise Science, multiple-output (MIMO), 620, octonions, gait analysis, Regression Analysis, Algorithms
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