Understanding Support Vector Machines with Polynomial Kernels

Interpreting models learned by a support vector machine (SVM) is often difficult, if not impossible, due to working in high-dimensional spaces. In this paper, we present an investigation into polynomial kernels for the SVM. We show that the models learned by these machines are constructed from terms related to the statistical moments of the support vectors. This allows us to deepen our understanding of the internal workings of these models and, for example, gauge the importance of combinations of features. We also discuss how the SVM with a quadratic kernel is related to the likelihood-ratio test for normally distributed populations.