Interpolation Kernel Machine and Indefinite Kernel Methods for Graph Classification Jiaqi Zhang 1 , Cheng-Lin Liu 2,3 , and Xiaoyi Jiang 1 1 Faculty of Mathematics and Computer Science, University of M¨ unster, Einsteinstrasse 62, 48149 M¨ unster, Germany 2 National Laboratory of Pattern Recognition, Institute of Automation of Chinese Academy of Sciences, Beijing 100190, P.R. China 3 School of Artificial Intelligence, University of Chinese Academy of Sciences, Beijing 10049, P.R. China 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. pos- itive 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 increas- ing the methodological plurality in the graph processing community. 1 Introduction Kernel-based methods in machine learning have sound mathematical foundation and provide powerful tools in numerous fields. In addition to classification and regression [7,22], they also have successfully contributed to other tasks such as clustering [34], dimensionality reduction (e.g. PCA [15]), consensus learning [25], computer vision [17], and recently to studying deep neural networks [10]. Graph kernels provide a way to compute similarities between graphs [13,16,27]. As such they can be used for graph classification, in particular with Support Vec- tor Machine (SVM) but not only. Graph kernels have been studied for a long time. In this work we address two aspects that are unexplored in the literature so far: interpolation kernel machine (IKM) and indefinite kernel methods. First, we will look at a particular class of kernel-based classification methods, the so-called IKM, which has undeservedly hardly received attention in the liter- ature. The recent work [3] brought it more attention in the research community and serves as the base of our work. Despite the diversity in the design of graph kernels, their use for classification is rather monotonous, namely by using sup- port vector machines (SVM). This is also reflected in the recent survey papers