A geometry-based two-step method for nonlinear classification using quasi-linear support vector machine

This paper proposes a two-step method to construct a nonlinear classifier consisting of multiple local linear classifiers interpolated with a basis function. In the first step, a geometry-based approach is first introduced to detect local linear partitions and build local linear classifiers. A coarse nonlinear classifier can then be constructed by interpolating the local linear classifiers. In the second step, a support vector machine (SVM) formulation is used to further implicitly optimize the linear parameters of the nonlinear classifier. In this way, the nonlinear classifier is constructed in exactly the same way as a standard SVM, using a special data-dependent quasi-linear kernel composed of the information of the local linear partitions. Numerical experiments on several real-world datasets demonstrate the effectiveness of the proposed classifier and show that, in cases where traditional nonlinear SVMs run into overfitting problems, the proposed classifier is effective in improving the classification performance.