Spatial-Temporal Data Modeling with Graph Neural Networks

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Spatial-temporal graph modeling is an important task to analyze the spatial relations and temporal trends of components in a system. It aims to model the dynamic node-level inputs by assuming inter-dependency between connected nodes. A basic assumption behind spatial-temporal graph modeling is that a node's future information is conditioned on its historical information as well as its neighbors' historical information. Therefore how to capture spatial and temporal dependencies simultaneously becomes a primary challenge. Current studies on spatial-temporal graph modeling face four major shortcomings: 1) Most graph neural networks only focus on the low frequency band of graph signals; 2) Current studies assume the graph structure of data reflects the genuine dependency relationships among nodes; 3) Existing studies on spatial-temporal graph neural networks are not applicable to pure multivariate time series data due to the absence of a predefined graph and lack of a general framework; 4) Existing approaches either model spatial-temporal dependencies locally or model spatial correlations and temporal correlations separately. The aim of this thesis is to study spatial-temporal data from the perspective of deep learning on graphs. I have studied the research objective in deep depth with four research questions: (1) How to coordinate the low, middle, and high frequency band of graph signals in graph convolution networks. (2) How to model spatial-temporal graph data effectively and efficiently; (3) How to handle spatial dependencies when a graph is totally missing, incomplete or inaccurate in spatial-temporal graph modeling; (4) In contrast to traditional spatial-temporal graph neural networks that handle spatial dependencies and temporal dependencies in separate, how to unify space and time as a whole in message passing. To address the aforementioned four research problems, I proposed four algorithms or models that can achieve satisfactory results. Specifically, I proposed an Automatic Graph Convolutional Network to learn graph frequency bands for graph convolution filters automatically; I introduced an efficient and effective framework that integrates diffusion graph convolution and dilated temporal convolution to capture spatial-temporal dependencies simultaneously. I developed a novel joint-learning algorithm that can capture spatial-temporal dependencies and learn latent graph structures at the same time; I designed a unified graph neural network that captures the inner spatial-temporal dependencies without compromising space-time integrity. To validate the proposed methods, I have conducted experiments on real-world datasets with a range of tasks including node classification, graph classification, and spatial-temporal graph forecasting. Experimental results demonstrate the effectiveness of the proposed methods.
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