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Learning representation on graph plays a crucial role in numerous tasks of pattern recognition. Different from grid-shaped images/videos, on which local convolution kernels can be lattices, however, graphs are fully coordinate-free on vertices and edges. In this work, we propose a Gaussian-induced convolution (GIC) framework to conduct local convolution filtering on irregular graphs. Specifically, an edge-induced Gaussian mixture model is designed to encode variations of subgraph region by integrating edge information into weighted Gaussian models, each of which implicitly characterizes one component of subgraph variations. In order to coarsen a graph, we derive a vertex-induced Gaussian mixture model to cluster vertices dynamically according to the connection of edges, which is approximately equivalent to the weighted graph cut. We conduct our multi-layer graph convolution network on several public datasets of graph classification. The extensive experiments demonstrate that our GIC is effective and can achieve the state-of-the-art results., Comment: 8 pages, 9 figures, AAAI-19 conference

Numerous pattern recognition applications can be formed as learning from graph-structured data, including social network, protein-interaction network, the world wide web data, knowledge graph, etc. While convolutional neural network (CNN) facilitates great advances in gridded image/video understanding tasks, very limited attention has been devoted to transform these successful network structures (including Inception net, Residual net, Dense net, etc.) to establish convolutional networks on graph, due to its irregularity and complexity geometric topologies (unordered vertices, unfixed number of adjacent edges/vertices). In this paper, we aim to give a comprehensive analysis of when work matters by transforming different classical network structures to graph CNN, particularly in the basic graph recognition problem. Specifically, we firstly review the general graph CNN methods, especially in its spectral filtering operation on the irregular graph data. We then introduce the basic structures of ResNet, Inception and DenseNet into graph CNN and construct these network structures on graph, named as G_ResNet, G_Inception, G_DenseNet. In particular, it seeks to help graph CNNs by shedding light on how these classical network structures work and providing guidelines for choosing appropriate graph network frameworks. Finally, we comprehensively evaluate the performance of these different network structures on several public graph datasets (including social networks and bioinformatic datasets), and demonstrate how different network structures work on graph CNN in the graph recognition task.

Graph classification is a fundamental but challenging issue for numerous real-world applications. Despite recent great progress in image/video classification, convolutional neural networks (CNNs) cannot yet cater to graphs well because of graphical non-Euclidean topology. In this work, we propose a walk-steered convolutional (WSC) network to assemble the essential success of standard convolutional neural networks as well as the powerful representation ability of random walk. Instead of deterministic neighbor searching used in previous graphical CNNs, we construct multi-scale walk fields (a.k.a. local receptive fields) with random walk paths to depict subgraph structures and advocate graph scalability. To express the internal variations of a walk field, Gaussian mixture models are introduced to encode principal components of walk paths therein. As an analogy to a standard convolution kernel on image, Gaussian models implicitly coordinate those unordered vertices/nodes and edges in a local receptive field after projecting to the gradient space of Gaussian parameters. We further stack graph coarsening upon Gaussian encoding by using dynamic clustering, such that high-level semantics of graph can be well learned like the conventional pooling on image. The experimental results on several public datasets demonstrate the superiority of our proposed WSC method over many state-of-the-arts for graph classification., Comment: 13 pages, 6 figures, 3 tables