Graph-Time Convolutional Neural Networks: Architecture and Theoretical Analysis

• URL: http://arxiv.org/abs/2206.15174v1
• Date: Thu, 30 Jun 2022 10:20:52 GMT
• Title: Graph-Time Convolutional Neural Networks: Architecture and Theoretical Analysis
• Authors: Mohammad Sabbaqi and Elvin Isufi
• Abstract summary: We introduce Graph-Time Convolutional Neural Networks (GTCNNs) as principled architecture to aid learning. The approach can work with any type of product graph and we also introduce a parametric graph to learn also the producttemporal coupling. Extensive numerical results on benchmark corroborate our findings and show the GTCNN compares favorably with state-of-the-art solutions.
• Score: 12.995632804090198
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Devising and analyzing learning models for spatiotemporal network data is of importance for tasks including forecasting, anomaly detection, and multi-agent coordination, among others. Graph Convolutional Neural Networks (GCNNs) are an established approach to learn from time-invariant network data. The graph convolution operation offers a principled approach to aggregate multiresolution information. However, extending the convolution principled learning and respective analysis to the spatiotemporal domain is challenging because spatiotemporal data have more intrinsic dependencies. Hence, a higher flexibility to capture jointly the spatial and the temporal dependencies is required to learn meaningful higher-order representations. Here, we leverage product graphs to represent the spatiotemporal dependencies in the data and introduce Graph-Time Convolutional Neural Networks (GTCNNs) as a principled architecture to aid learning. The proposed approach can work with any type of product graph and we also introduce a parametric product graph to learn also the spatiotemporal coupling. The convolution principle further allows a similar mathematical tractability as for GCNNs. In particular, the stability result shows GTCNNs are stable to spatial perturbations but there is an implicit trade-off between discriminability and robustness; i.e., the more complex the model, the less stable. Extensive numerical results on benchmark datasets corroborate our findings and show the GTCNN compares favorably with state-of-the-art solutions. We anticipate the GTCNN to be a starting point for more sophisticated models that achieve good performance but are also fundamentally grounded.

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