Geometric Intuition and Algorithms for Ev--SVM

Álvaro Barbero; Akiko Takeda; Jorge López

In this work we address the E

$\nu$ --SVM model proposed by PÃ©rez --Cruz et al. as an extension of the traditional

$\nu$ support vector classification model (

$\nu$ --SVM). Through an enhancement of the range of admissible values for the regularization parameter

$\nu$ , the E

$\nu$ --SVM has been shown to be able to produce a wider variety of decision functions, giving rise to a better adaptability to the data. However, while a clear and intuitive geometric interpretation can be given for the

$\nu$ --SVM model as a nearest--point problem in reduced convex hulls (RCH--NPP), no previous work has been made in developing such intuition for the E

$\nu$ --SVM model. In this paper we show how E

$\nu$ --SVM can be reformulated as a geometrical problem that generalizes RCH--NPP, providing new insights into this model. Under this novel point of view, we propose the rapminos algorithm, able to solve E

$\nu$ --SVM more efficiently than the current methods. Furthermore, we show how rapminos is able to address the E

$\nu$ --SVM model for any choice of regularization norm

$\ell_{p \geq 1}$ seamlessly, which further extends the SVM model flexibility beyond the usual E

$\nu$ --SVM models.

Geometric Intuition and Algorithms for Ev--SVM

Abstract