Topological Elastic Graph Convolutional Networks for Spatial-Temporal Sequence Forecasting

Spatial-temporal sequence prediction is a hotspot problem, which is very important to the development of society. Due to the complexity and mutual influence of different regions, spatial-temporal data has complicated and dynamic spatial-temporal correlation. How to effectively capture the underlying information from data to get better predictions becomes a challenge. Current work often involves a given graph structure to build spatial dependency, but it ignores the dynamic trend and context information of data. The potential spatiotemporal dependence obtained through the similarity of time series is easily affected by external factors and it is not robust. The graph convolutional network has been proven to be a global smoothing low-pass filter, which lacks the ability of local smoothing and obtaining high-frequency information. Therefore, we proposed spatial-temporal topological elastic graph convolutional networks (STTEGCN), firstly persistent homology is introduced to acquire the topological correlation and to acquire a topological graph that can better express the potential correlation between data. Introduce an elastic message-passing mechanism to obtain global and local adaptive smoothing ability. At the same time, the high-frequency filter is used to obtain useful high-frequency information, and then mining more efficient and valuable information expression. The gated hybrid dilated convolution is put forward to strengthen the capability of the model to obtain long and short temporal features, so as to boost the predictability of the model. We conducted experimental simulations on multiple public transportation and meteorological data. The results indicated that STTEGCN has the most advanced behavior over other baselines.