Abstract

We describe the role of generalized support vector machines in separating massive and complex data using arbitrary nonlinear kernels. Feature selection that improves generalization is implemented via an effective procedure that utilizes a polyhedral norm or a concave function minimization. Massive data is separated using a linear programming chunking algorithm as well as a successive overrelaxation algorithm, each of which is capable of processing data with millions of points. 1 2 1. INTRODUCTION We address here the problem of classifying data in n-dimensional real (Euclidean) space R n into one of two disjoint nite point sets (i.e. classes). The support vector machine (SVM) approach to classication [57, 2, 25, 58, 13, 54, 55] attempts to separate points belonging to two given sets in R n by a nonlinear surface, often only implicitly dened by a kernel function. Since the nonlinear surface in R n is typically linear in its parameters, it can be represented as a linear func...

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