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ItemA monomial ν-SV method for regressionSHILTON, ALISTAIR ; Lai, Daniel ; PALANISWAMI, MARIMUTHU ( 2007)In the present paper we describe a new formulation for Support Vector regression (SVR), namely monomial ν-SVR. Like the standard ν-SVR, the monomial ν-SVR method automatically adjusts the radius of insensitivity (the tube width, epsilon) to suit the training data. However, by replacing Vapnik’s epsilon-insensitive cost with a more general monomial epsilon-insensitive cost (and likewise replacing the linear tube shrinking term with a monomial tube shrinking term), the performance of the monomial ν-SVR is improved for data corrupted by a wider range of noise distributions. We focus on the quadric form of monomial ν-SVR and show that the dual form of this is simpler than the standard ν-SVR. We show that, like Suykens’ Least-Squares SVR (LS-SVR) method (and unlike standard ν-SVR), the quadric ν-SVR dual has a unique global solution. Comparisons are made between the asymptotic efficiency of our method and that of standard ν-SVR and LS-SVR which demonstrate the superiority of our method for the special case of higher order polynomial noise. These theoretical predictions are validated using experimental comparisons with the alternative approaches of standard ν-SVR, LS-SVR and weighted LS-SVR.
ItemMercer's theorem for quaternionic kernelsSHILTON, ALISTAIR ( 2007)An extension of Mercer’s theorem to quaternionic valued kernel functions with applications in the field of machine learningis presented.