Support vector machines with piecewise linear feature mapping

As the simplest extension to linear classifiers, piecewise linear (PWL) classifiers have attracted a lot of attention, because of their simplicity and classification capability. In this paper, a PWL feature mapping is introduced by investigating the property of the PWL classification boundary. Then support vector machines (SVM) with PWL feature mappings are proposed, called PWL-SVMs. In this paper, it is shown that some widely used PWL classifiers, such as k-nearest-neighbor, adaptive boosting of linear classifier and intersection kernel support vector machine, can be represented by the proposed feature mapping. That means the proposed PWL-SVMs at least can achieve the performance of the above PWL classifiers. Moreover, PWL-SVMs enjoy good properties of SVM and the performance on numerical experiments illustrates the effectiveness. Then some extensions are discussed and the application of PWL-SVMs can be expected.