Numerous important problems can be framed as learning from graph data. We propose a framework for learning convolutional neural networks for arbitrary graphs. These graphs may be undirected, directed, and with both discrete and continuous node and edge attributes. Analogous to image-based convolutional networks that operate on locally connected regions of the input, we present a general approach to extracting locally connected regions from graphs. Using established benchmark data sets, we demonstrate that the learned feature representations are competitive with state of the art graph kernels and that their computation is highly efficient.
Recent work extended CNNs to topologies that differ from the low-dimensional grid structure @cite_31 @cite_17 . All of these methods, however, assume one global graph structure, that is, a correspondence of the vertices across input examples. @cite_11 perform convolutional type operations on graphs, developing a differentiable variant of one specific graph feature.
@cite_31 @cite_11 @cite_17
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This paper introduces a generalization of Convolutional Neural Networks (CNNs) to graphs with irregular linkage structures, especially heterogeneous graphs with typed nodes and schemas. We propose a novel spatial convolution operation to model the key properties of local connectivity and translation invariance, using high-order connection patterns or motifs. We develop a novel deep architecture Motif-CNN that employs an attention model to combine the features extracted from multiple patterns, thus effectively capturing high-order structural and feature information. Our experiments on semi-supervised node classification on real-world social networks and multiple representative heterogeneous graph datasets indicate significant gains of 6-21 over existing graph CNNs and other state-of-the-art techniques. In this work, we are interested in generalizing convolutional neural networks (CNNs) from low-dimensional regular grids, where image, video and speech are represented, to high-dimensional irregular domains, such as social networks, brain connectomes or words' embedding, represented by graphs. We present a formulation of CNNs in the context of spectral graph theory, which provides the necessary mathematical background and efficient numerical schemes to design fast localized convolutional filters on graphs. Importantly, the proposed technique offers the same linear computational complexity and constant learning complexity as classical CNNs, while being universal to any graph structure. Experiments on MNIST and 20NEWS demonstrate the ability of this novel deep learning system to learn local, stationary, and compositional features on graphs. In this work, we are interested in generalizing convolutional neural networks (CNNs) from low-dimensional regular grids, where image, video and speech are represented, to high-dimensional irregular domains, such as social networks, brain connectomes or words' embedding, represented by graphs. We present a formulation of CNNs in the context of spectral graph theory, which provides the necessary mathematical background and efficient numerical schemes to design fast localized convolutional filters on graphs. Importantly, the proposed technique offers the same linear computational complexity and constant learning complexity as classical CNNs, while being universal to any graph structure. Experiments on MNIST and 20NEWS demonstrate the ability of this novel deep learning system to learn local, stationary, and compositional features on graphs. Graph convolutional neural networks (Graph-CNNs) extend traditional CNNs to handle data that is supported on a graph. Major challenges when working with data on graphs are that the support set (the vertices of the graph) do not typically have a natural ordering, and in general, the topology of the graph is not regular (i.e., vertices do not all have the same number of neighbors). Thus, Graph-CNNs have huge potential to deal with 3D point cloud data which has been obtained from sampling a manifold. In this paper we develop a Graph-CNN for classifying 3D point cloud data, called PointGCN1. The architecture combines localized graph convolutions with two types of graph downsampling operations (also known as pooling). By the effective exploration of the point cloud local structure using the Graph-CNN, the proposed architecture achieves competitive performance on the 3D object classification benchmark ModelNet, and our architecture is more stable than competing schemes.