Geometric intuition and algorithms for Ev-SVM

In this work we address the Eν–SVM model proposed by Pérez–Cruz et al. as an extension of the traditional ν support vector classification model (ν–SVM). Through an enhancement of the range of admissible values for the regularization parameter ν, the Eν–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 ν–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 Eν– SVM model. In this paper we show how Eν–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 Eν–SVM more efficiently than the current methods. Furthermore, we show how RapMinos is able to address the Eν–SVM model for any choice of regularization norm `p≥1 seamlessly, which further extends the SVM model flexibility beyond the usual Eν–SVM models.