Interpolation Kernel Machine and Indefinite Kernel Methods for Graph Classification

Abstract

Graph kernels have been studied for a long time and applied among others for graph classification. In this paper we bring two novel aspects into the graph processing community. Currently, the backbone for kernel-based classification is solely the support vector machine. We introduce the interpolation kernel machine for this purpose. In addition, for both support vector machine and interpolation kernel machine, many kernels used in practice do not satisfy the formal requirements (e.g. positive definiteness). We thus introduce extensions of the standard version to indefinite kernel methods. We argue and experimentally demonstrate why these two aspects should be considered for graph classification. One of our conclusions will be that the interpolation kernel machine is a good alternative of support vector machine. Consequently, we will propose an extended experimental protocol. With this work we contribute to increasing the methodological plurality in the graph processing community.

Quadratic Kernel Learning for Interpolation Kernel Machine Based Graph Classification

“…In particular, restricting the weights to a small interval [0, 1] turns out to be positive. The matrix perturbation method, however, is not bestperforming among the methods studied in [31] to deal with indefinite kernels. Instead, a cross-entropy variant proved to be most favorable.…”

“…Thus, we need an indefinite interpolation kernel machine learning method for step 1 of the two-step optimization. Several methods for such an extension have been studied in [31]. We will use the matrix perturbation method in this work.…”

“…The study [3] demonstrated that interpolation kernel machines trained to have zero training error do perform very well on test data (a phenomenon typically observed in over-parametrized deep learning models). Our recent work [30] has shown that interpolation kernel machines are a good alternative to SVM for graph classification. This study justifies a systematic consideration of interpolation kernel machines parallel to the popular SVM for experimentation in graph classification.…”

“…This study justifies a systematic consideration of interpolation kernel machines parallel to the popular SVM for experimentation in graph classification. For this purpose we have proposed an extended experimental protocol in [30] to obtain the maximal possible graph classification performance in a particular application.…”

Interpolation Kernel Machines: Reducing Multiclass to Binary

“…They turned out to be a good alternative to DNNs, capable of matching and even surpassing their performance while utilizing less computational resources in training [15]. The recent work [29] has shown that interpolation kernel machines are also a good alternative to support vector machines (SVM).…”