Graph kernels have attracted a lot of attention during the last decade, and have evolved into a rapidly developing branch of learning on structured data. During the past 20 years, the considerable research activity that occurred in the field resulted in the development of dozens of graph kernels, each focusing on specific structural properties of graphs. Graph kernels have proven successful in a wide range of domains, ranging from social networks to bioinformatics. The goal of this survey is to provide a unifying view of the literature on graph kernels. In particular, we present a comprehensive overview of a wide range of graph kernels. Furthermore, we perform an experimental evaluation of several of those kernels on publicly available datasets, and provide a comparative study. Finally, we discuss key applications of graph kernels, and outline some challenges that remain to be addressed.
Graph kernels have become an established and widely-used technique for solving classification tasks on graphs. This survey gives a comprehensive overview of techniques for kernel-based graph classification developed in the past 15 years. We describe and categorize graph kernels based on properties inherent to their design, such as the nature of their extracted graph features, their method of computation and their applicability to problems in practice. In an extensive experimental evaluation, we study the classification accuracy of a large suite of graph kernels on established benchmarks as well as new datasets. We compare the performance of popular kernels with several baseline methods and study the effect of applying a Gaussian RBF kernel to the metric induced by a graph kernel. In doing so, we find that simple baselines become competitive after this transformation on some datasets. Moreover, we study the extent to which existing graph kernels agree in their predictions (and prediction errors) and obtain a data-driven categorization of kernels as result. Finally, based on our experimental results, we derive a practitioner's guide to kernel-based graph classification.
Nikolentzos, Giannis (Ecole Polytechnique and Athens University of Economics and Business) | Meladianos, Polykarpos (Ecole Polytechnique and Athens University of Economics and Business) | Vazirgiannis, Michalis (Ecole Polytechnique and Athens University of Economics and Business)
Graph kernels have emerged as a powerful tool for graph comparison. Most existing graph kernels focus on local properties of graphs and ignore global structure. In this paper, we compare graphs based on their global properties as these are captured by the eigenvectors of their adjacency matrices. We present two algorithms for both labeled and unlabeled graph comparison. These algorithms represent each graph as a set of vectors corresponding to the embeddings of its vertices. The similarity between two graphs is then determined using the Earth Mover's Distance metric. These similarities do not yield a positive semidefinite matrix. To address for this, we employ an algorithm for SVM classification using indefinite kernels. We also present a graph kernel based on the Pyramid Match kernel that finds an approximate correspondence between the sets of vectors of the two graphs. We further improve the proposed kernel using the Weisfeiler-Lehman framework. We evaluate the proposed methods on several benchmark datasets for graph classification and compare their performance to state-of-the-art graph kernels. In most cases, the proposed algorithms outperform the competing methods, while their time complexity remains very attractive.
Graph kernels have recently emerged as a promising approach for tackling the graph similarity and learning tasks at the same time. In this paper, we propose a general framework for designing graph kernels. The proposed framework capitalizes on the well-known message passing scheme on graphs. The kernels derived from the framework consist of two components. The first component is a kernel between vertices, while the second component is a kernel between graphs. The main idea behind the proposed framework is that the representations of the vertices are implicitly updated using an iterative procedure. Then, these representations serve as the building blocks of a kernel that compares pairs of graphs. We derive four instances of the proposed framework, and show through extensive experiments that these instances are competitive with state-of-the-art methods in various tasks.
We propose graph kernels based on subgraph matchings, i.e. structure-preserving bijections between subgraphs. While recently proposed kernels based on common subgraphs (Wale et al., 2008; Shervashidze et al., 2009) in general can not be applied to attributed graphs, our approach allows to rate mappings of subgraphs by a flexible scoring scheme comparing vertex and edge attributes by kernels. We show that subgraph matching kernels generalize several known kernels. To compute the kernel we propose a graph-theoretical algorithm inspired by a classical relation between common subgraphs of two graphs and cliques in their product graph observed by Levi (1973). Encouraging experimental results on a classification task of real-world graphs are presented.