Geometric Characterization Of Piecewise Linear And Quadratic Ev-SVM

Recent years, support vector machines(SVM) has become a very sophisticated algorithm in the field of data analysis. With the support vector machine algorithm constantly depth study, the field has appeared v-SVM, V-SVM, and a variety of the promotion of other nuclear functions. Simultaneously, the geometric interprentation for the type of SVM algorithm has been emphasized. Geometric interpretation can not only deepen the understanding of the nature of the algorithm, but also help to improve the algorithm and proposed more new efficient algorithms.In this paper, for the more complex sample space which is can’t be linear classified,the whole region is divided into a plurality of projections,giving piecewise linear and piecewise quadratic classification algorithm in the projection centralized application of SVM. We have found a suitable clustering algorithm for initial sample space division according to the different characteristics of the data. Using the existing convex hull construction method, we give the piecewise linear Ev-SVM model on the local convex hull to prove the equivalence piecewise linear Ev-SVM with the corresponding ERCH-Margin model in the local convex hull. Thereby giving global equivalence, we prove the dual relationship between the ERCH-Margin model and ERCH-NPP model. We will also study the problem of quadratic classifier corresponding case. By using a similar method we will came to similar conclusions about piecewise linear quadratic Ev-SVM classifier.