Scalable kernels for graphs with continuous attributes

While graphs with continuous node attributes arise in many applications, state-of-the-art graph kernels for comparing continuous-attributed graphs suffer from a high runtime complexity. For instance, the popular shortest path kernel scales as O(n4), where n is the number of nodes. In this paper, we present a class of graph kernels with computational complexity O(n 2(m+log n+δ2 +d)), where is the graph diameter, m is the number of edges, and d is the dimension of the node attributes. Due to the sparsity and small diameter of real-world graphs, these kernels typically scale comfortably to large graphs. In our experiments, the presented kernels outperform state-of-the-art kernels in terms of speed and accuracy on classification benchmark datasets

Learning from graphs with structural variation

We study the effect of structural variation in graph data on the predictive performance of graph kernels. To this end, we introduce a novel, noise-robust adaptation of the GraphHopper kernel and validate it on benchmark data, obtaining modestly improved predictive performance on a range of datasets. Next, we investigate the performance of the state-of-the-art Weisfeiler-Lehman graph kernel under increasing synthetic structural errors and find that the effect of introducing errors depends strongly on the dataset.Comment: Presented at the NIPS 2017 workshop "Learning on Distributions, Functions, Graphs and Groups

A Survey on Graph Kernels

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

A tree-based kernel for graphs with continuous attributes

The availability of graph data with node attributes that can be either discrete or real-valued is constantly increasing. While existing kernel methods are effective techniques for dealing with graphs having discrete node labels, their adaptation to non-discrete or continuous node attributes has been limited, mainly for computational issues. Recently, a few kernels especially tailored for this domain, and that trade predictive performance for computational efficiency, have been proposed. In this paper, we propose a graph kernel for complex and continuous nodes' attributes, whose features are tree structures extracted from specific graph visits. The kernel manages to keep the same complexity of state-of-the-art kernels while implicitly using a larger feature space. We further present an approximated variant of the kernel which reduces its complexity significantly. Experimental results obtained on six real-world datasets show that the kernel is the best performing one on most of them. Moreover, in most cases the approximated version reaches comparable performances to current state-of-the-art kernels in terms of classification accuracy while greatly shortening the running times.Comment: This work has been submitted to the IEEE Transactions on Neural Networks and Learning Systems for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

Propagation Kernels

We introduce propagation kernels, a general graph-kernel framework for efficiently measuring the similarity of structured data. Propagation kernels are based on monitoring how information spreads through a set of given graphs. They leverage early-stage distributions from propagation schemes such as random walks to capture structural information encoded in node labels, attributes, and edge information. This has two benefits. First, off-the-shelf propagation schemes can be used to naturally construct kernels for many graph types, including labeled, partially labeled, unlabeled, directed, and attributed graphs. Second, by leveraging existing efficient and informative propagation schemes, propagation kernels can be considerably faster than state-of-the-art approaches without sacrificing predictive performance. We will also show that if the graphs at hand have a regular structure, for instance when modeling image or video data, one can exploit this regularity to scale the kernel computation to large databases of graphs with thousands of nodes. We support our contributions by exhaustive experiments on a number of real-world graphs from a variety of application domains