Experiments in Piecewise Linear Approximation of Nonlinear Class Boundaries using Support Vector Machines

This work is concerned with issues that arise in implementation of support vector machines (SVM) for detecting class boundaries. First, an exact solution for the convex optimization problem for Support Vector Machines(SVM) without any conventional heuristic optimization techniques is considered. Second, the application of this solution in an iterative SVM algorithm with linear kernels to data sets which are not linearly separable in order to obtain piecewise linear approximations of the class boundaries for such data. Finally, for nonlinearly separable data, the approach is applied in a space obtained by a suitable nonlinear transformation of the data, which does not increase the dimensionality of the feature space, in such a way so as to recover nonlinear class boundaries. The proposed approach is illustrated on several two-dimensional artificial datasets.