Graphlet Count Estimation via Convolutional Neural Networks

International audienceGraphlets are defined as k-node connected induced subgraph patterns. For instance, for an undirected graph, 3-node graphlets include close triangle and open triangle. The number of each graphlet, called graphlet count, is a signature which characterizes the local network structure of a given graph. Graphlet count plays a prominent role in network analysis of many fields, most notably bioinformatics and social science. However, computing exact graphlet count is inherently difficult and computational expensive because the number of graphlets growsexponentially large as the graph size and/or graphlet size grow. To deal with this difficulty, many sampling methods were proposed to estimate graphlet count with bounded error. Nevertheless, these methods require large number of samples to be statistically reliable, which is still computationally demanding. Intuitively, learning from historic graphs can make estimation more accurate and avoid many repetitive counting to reduce computational cost. Based on this idea, we propose a convolutional neural network (CNN) framework and two preprocessing techniques to estimate graphlet count. Extensive experiments on two types of random graphs and real world biochemistry graphs show that our framework can offer substantial speedup on estimating graphlet count of new graphs with high accuracy

Learning to count: A deep learning framework for graphlet count estimation

International audienceGraphlet counting is a widely-explored problem in network analysis and has been successfully applied to a variety of applications in many domains, most notatbly bioinformatics, social science and infrastructure network studies. Efficiently computing graphlet counts remains challenging due to the combinatorial explosion, where a naive enumeration algorithm needs O($N^k$) time for $k$-node graphlets in a network of size $N$.Recently, many works introduced carefully designed combinatorial and sampling methods with encouraging results. However, the existing methods ignore the fact that graphlet counts and the graph structural information are correlated. They always consider a graph as a new input and repeat the tedious counting procedure on a regular basis even if it is similar or exactly isomorphic to previously studied graphs. This provides an opportunity to speed up the graphlet count estimation procedure by exploiting this correlation via learning methods. In this paper, we raise a novel Graphlet Count Learning (GCL) problem: given a set of historical graphs with known graphlet counts, how to learn to estimate/predict graphlet count for unseen graphs coming from the same (or similar) underlying distribution. We develop a deep learning framework which contains two {\em convolutional neural network} (CNN) models and a series of data {\em preprocessing techniques} to solve the GCL problem. Extensive experiments are conducted on three types of synthetic random graphs and three types of real world graphs for all 3,4,5-node graphlets to demonstrate the accuracy, efficiency and generalizability of our framework. Compared with state-of-the-art exact/sampling methods, our framework shows great potential, which can offer up to two orders of magnitude speedup on synthetic graphs and achieves on par speed on real world graphs with competitive accuracy

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