Spatial-temporal data, fundamental to many intelligent applications, reveals dependencies indicating causal links between present measurements at specific locations and historical data at the same or other locations. Within this context, adaptive spatial-temporal graph neural networks (ASTGNNs) have emerged as valuable tools for modelling these dependencies, especially through a data-driven approach rather than pre-defined spatial graphs. While this approach offers higher accuracy, it presents increased computational demands. Addressing this challenge, this paper delves into the concept of localisation within ASTGNNs, introducing an innovative perspective that spatial dependencies should be dynamically evolving over time. We introduce \textit{DynAGS}, a localised ASTGNN framework aimed at maximising efficiency and accuracy in distributed deployment. This framework integrates dynamic localisation, time-evolving spatial graphs, and personalised localisation, all orchestrated around the Dynamic Graph Generator, a light-weighted central module leveraging cross attention. The central module can integrate historical information in a node-independent manner to enhance the feature representation of nodes at the current moment. This improved feature representation is then used to generate a dynamic sparse graph without the need for costly data exchanges, and it supports personalised localisation. Performance assessments across two core ASTGNN architectures and nine real-world datasets from various applications reveal that \textit{DynAGS} outshines current benchmarks, underscoring that the dynamic modelling of spatial dependencies can drastically improve model expressibility, flexibility, and system efficiency, especially in distributed settings.

In this paper, we present a novel method to significantly enhance the computational efficiency of Adaptive Spatial-Temporal Graph Neural Networks (ASTGNNs) by introducing the concept of the Graph Winning Ticket (GWT), derived from the Lottery Ticket Hypothesis (LTH). By adopting a pre-determined star topology as a GWT prior to training, we balance edge reduction with efficient information propagation, reducing computational demands while maintaining high model performance. Both the time and memory computational complexity of generating adaptive spatial-temporal graphs is significantly reduced from $\mathcal{O}(N^2)$ to $\mathcal{O}(N)$. Our approach streamlines the ASTGNN deployment by eliminating the need for exhaustive training, pruning, and retraining cycles, and demonstrates empirically across various datasets that it is possible to achieve comparable performance to full models with substantially lower computational costs. Specifically, our approach enables training ASTGNNs on the largest scale spatial-temporal dataset using a single A6000 equipped with 48 GB of memory, overcoming the out-of-memory issue encountered during original training and even achieving state-of-the-art performance. Furthermore, we delve into the effectiveness of the GWT from the perspective of spectral graph theory, providing substantial theoretical support. This advancement not only proves the existence of efficient sub-networks within ASTGNNs but also broadens the applicability of the LTH in resource-constrained settings, marking a significant step forward in the field of graph neural networks. Code is available at https://anonymous.4open.science/r/paper-1430.

Spatial-temporal graph models are prevailing for abstracting and modelling spatial and temporal dependencies. In this work, we ask the following question: whether and to what extent can we localise spatial-temporal graph models? We limit our scope to adaptive spatial-temporal graph neural networks (ASTGNNs), the state-of-the-art model architecture. Our approach to localisation involves sparsifying the spatial graph adjacency matrices. To this end, we propose Adaptive Graph Sparsification (AGS), a graph sparsification algorithm which successfully enables the localisation of ASTGNNs to an extreme extent (fully localisation). We apply AGS to two distinct ASTGNN architectures and nine spatial-temporal datasets. Intriguingly, we observe that spatial graphs in ASTGNNs can be sparsified by over 99.5\% without any decline in test accuracy. Furthermore, even when ASTGNNs are fully localised, becoming graph-less and purely temporal, we record no drop in accuracy for the majority of tested datasets, with only minor accuracy deterioration observed in the remaining datasets. However, when the partially or fully localised ASTGNNs are reinitialised and retrained on the same data, there is a considerable and consistent drop in accuracy. Based on these observations, we reckon that \textit{(i)} in the tested data, the information provided by the spatial dependencies is primarily included in the information provided by the temporal dependencies and, thus, can be essentially ignored for inference; and \textit{(ii)} although the spatial dependencies provide redundant information, it is vital for the effective training of ASTGNNs and thus cannot be ignored during training. Furthermore, the localisation of ASTGNNs holds the potential to reduce the heavy computation overhead required on large-scale spatial-temporal data and further enable the distributed deployment of ASTGNNs.

Spatiotemporal learning, which aims at extracting spatiotemporal correlations from the collected spatiotemporal data, is a research hotspot in recent years. And considering the inherent graph structure of spatiotemporal data, recent works focus on capturing spatial dependencies by utilizing Graph Convolutional Networks (GCNs) to aggregate vertex features with the guidance of adjacency matrices. In this paper, with extensive and deep-going experiments, we comprehensively analyze existing spatiotemporal graph learning models and reveal that extracting adjacency matrices with carefully design strategies, which are viewed as the key of enhancing performance on graph learning, are largely ineffective. Meanwhile, based on these experiments, we also discover that the aggregation itself is more important than the way that how vertices are aggregated. With these preliminary, a novel efficient Graph-Free Spatial (GFS) learning module based on layer normalization for capturing spatial correlations in spatiotemporal graph learning. The proposed GFS module can be easily plugged into existing models for replacing all graph convolution components. Rigorous theoretical proof demonstrates that the time complexity of GFS is significantly better than that of graph convolution operation. Extensive experiments verify the superiority of GFS in both the perspectives of efficiency and learning effect in processing graph-structured data especially extreme large scale graph data.

The technology of traffic flow forecasting plays an important role in intelligent transportation systems. Based on graph neural networks and attention mechanisms, most previous works utilize the transformer architecture to discover spatiotemporal dependencies and dynamic relationships. However, they have not considered correlation information among spatiotemporal sequences thoroughly. In this paper, based on the maximal information coefficient, we present two elaborate spatiotemporal representations, spatial correlation information (SCorr) and temporal correlation information (TCorr). Using SCorr, we propose a correlation information-based spatiotemporal network (CorrSTN) that includes a dynamic graph neural network component for integrating correlation information into spatial structure effectively and a multi-head attention component for modeling dynamic temporal dependencies accurately. Utilizing TCorr, we explore the correlation pattern among different periodic data to identify the most relevant data, and then design an efficient data selection scheme to further enhance model performance. The experimental results on the highway traffic flow (PEMS07 and PEMS08) and metro crowd flow (HZME inflow and outflow) datasets demonstrate that CorrSTN outperforms the state-of-the-art methods in terms of predictive performance. In particular, on the HZME (outflow) dataset, our model makes significant improvements compared with the ASTGNN model by 12.7%, 14.4% and 27.4% in the metrics of MAE, RMSE and MAPE, respectively.