Tensor graph convolutional neural network

In this paper, we propose a novel tensor graph convolutional neural network (TGCNN) to conduct convolution on factorizable graphs, for which here two types of problems are focused, one is sequential dynamic graphs and the other is cross-attribute graphs. Especially, we propose a graph preserving layer to memorize salient nodes of those factorized subgraphs, i.e. cross graph convolution and graph pooling. For cross graph convolution, a parameterized Kronecker sum operation is proposed to generate a conjunctive adjacency matrix characterizing the relationship between every pair of nodes across two subgraphs. Taking this operation, then general graph convolution may be efficiently performed followed by the composition of small matrices, which thus reduces high memory and computational burden. Encapsuling sequence graphs into a recursive learning, the dynamics of graphs can be efficiently encoded as well as the spatial layout of graphs. To validate the proposed TGCNN, experiments are conducted on skeleton action datasets as well as matrix completion dataset. The experiment results demonstrate that our method can achieve more competitive performance with the state-of-the-art methods

Spatial-Temporal Tensor Graph Convolutional Network for Traffic Prediction

Accurate traffic prediction is crucial to the guidance and management of urban traffics. However, most of the existing traffic prediction models do not consider the computational burden and memory space when they capture spatial-temporal dependence among traffic data. In this work, we propose a factorized Spatial-Temporal Tensor Graph Convolutional Network to deal with traffic speed prediction. Traffic networks are modeled and unified into a graph that integrates spatial and temporal information simultaneously. We further extend graph convolution into tensor space and propose a tensor graph convolution network to extract more discriminating features from spatial-temporal graph data. To reduce the computational burden, we take Tucker tensor decomposition and derive factorized a tensor convolution, which performs separate filtering in small-scale space, time, and feature modes. Besides, we can benefit from noise suppression of traffic data when discarding those trivial components in the process of tensor decomposition. Extensive experiments on two real-world traffic speed datasets demonstrate our method is more effective than those traditional traffic prediction methods, and meantime achieves state-of-the-art performance

Classifying Signals on Irregular Domains via Convolutional Cluster Pooling

We present a novel and hierarchical approach for supervised classification of signals spanning over a fixed graph, reflecting shared properties of the dataset. To this end, we introduce a Convolutional Cluster Pooling layer exploiting a multi-scale clustering in order to highlight, at different resolutions, locally connected regions on the input graph. Our proposal generalises well-established neural models such as Convolutional Neural Networks (CNNs) on irregular and complex domains, by means of the exploitation of the weight sharing property in a graph-oriented architecture. In this work, such property is based on the centrality of each vertex within its soft-assigned cluster. Extensive experiments on NTU RGB+D, CIFAR-10 and 20NEWS demonstrate the effectiveness of the proposed technique in capturing both local and global patterns in graph-structured data out of different domains.Comment: 12 pages, 6 figures. To appear in the Proceedings of the 22nd International Conference on Artificial Intelligence and Statistics (AISTATS) 2019, Naha, Okinawa, Japan. PMLR: Volume 8

Graph Prolongation Convolutional Networks: Explicitly Multiscale Machine Learning on Graphs with Applications to Modeling of Cytoskeleton

We define a novel type of ensemble Graph Convolutional Network (GCN) model. Using optimized linear projection operators to map between spatial scales of graph, this ensemble model learns to aggregate information from each scale for its final prediction. We calculate these linear projection operators as the infima of an objective function relating the structure matrices used for each GCN. Equipped with these projections, our model (a Graph Prolongation-Convolutional Network) outperforms other GCN ensemble models at predicting the potential energy of monomer subunits in a coarse-grained mechanochemical simulation of microtubule bending. We demonstrate these performance gains by measuring an estimate of the FLOPs spent to train each model, as well as wall-clock time. Because our model learns at multiple scales, it is possible to train at each scale according to a predetermined schedule of coarse vs. fine training. We examine several such schedules adapted from the Algebraic Multigrid (AMG) literature, and quantify the computational benefit of each. We also compare this model to another model which features an optimized coarsening of the input graph. Finally, we derive backpropagation rules for the input of our network model with respect to its output, and discuss how our method may be extended to very large graphs.Comment: Revised version submitted to IOP: Machine Learning, Science, and Technolog

Graph Neural Networks: Taxonomy, Advances and Trends

Graph neural networks provide a powerful toolkit for embedding real-world graphs into low-dimensional spaces according to specific tasks. Up to now, there have been several surveys on this topic. However, they usually lay emphasis on different angles so that the readers can not see a panorama of the graph neural networks. This survey aims to overcome this limitation, and provide a comprehensive review on the graph neural networks. First of all, we provide a novel taxonomy for the graph neural networks, and then refer to up to 400 relevant literatures to show the panorama of the graph neural networks. All of them are classified into the corresponding categories. In order to drive the graph neural networks into a new stage, we summarize four future research directions so as to overcome the facing challenges. It is expected that more and more scholars can understand and exploit the graph neural networks, and use them in their research community.Comment: 42 pages, 7 figure