Learning SVM Classifiers with Indefinite Kernels

Recently, training support vector machines with indefinite kernels has attracted great attention in the machine learning community. In this paper, we tackle this problem by formulating a joint optimization model over SVM classifications and kernel principal component analysis. We first reformulate the kernel principal component analysis as a general kernel transformation framework, and then incorporate it into the SVM classification to formulate a joint optimization model. The proposed model has the advantage of making consistent kernel transformations over training and test samples. It can be used for both binary classification and multi-class classification problems. Our experimental results on both synthetic data sets and real world data sets show the proposed model can significantly outperform related approaches.