# Fully-Connected Spatial-Temporal Graph for Multivariate Time-Series Data

arXiv: https://arxiv.org/abs/2309.05305 · HTML: https://mlsanity.com/paper/2309.05305/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 38 references that are in the map.
- First posted on arXiv 11 Sep 2023.

## Builds on (most cited first, 16 of 16)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks](https://mlsanity.com/paper/2005.11650/) (2020)
- [A Transformer-based Framework for Multivariate Time Series Representation Learning](https://mlsanity.com/paper/2010.02803/) (2020)
- [Time-Series Representation Learning via Temporal and Contextual Contrasting](https://mlsanity.com/paper/2106.14112/) (2021)
- [Graph Neural Network-Based Anomaly Detection in Multivariate Time Series](https://mlsanity.com/paper/2106.06947/) (2021)
- [Unsupervised Scalable Representation Learning for Multivariate Time Series](https://mlsanity.com/paper/1901.10738/) (2019)
- [A Survey on Graph Neural Networks for Time Series: Forecasting, Classification, Imputation, and Anomaly Detection](https://mlsanity.com/paper/2307.03759/) (2023)
- [Pre-training Enhanced Spatial-temporal Graph Neural Network for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2206.09113/) (2022)
- [Multi-Scale Adaptive Graph Neural Network for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2201.04828/) (2022)
- [Approaches and Applications of Early Classification of Time Series: A Review](https://mlsanity.com/paper/2005.02595/) (2020)
- [MHCCL: Masked Hierarchical Cluster-Wise Contrastive Learning for Multivariate Time Series](https://mlsanity.com/paper/2212.01141/) (2022)
- [DSTP-RNN: a dual-stage two-phase attention-based recurrent neural networks for long-term and multivariate time series prediction](https://mlsanity.com/paper/1904.07464/) (2019)

## Built on by (most cited first, 23 of 23)

- [A Comprehensive Survey of Deep Learning for Multivariate Time Series Forecasting: A Channel Strategy Perspective](https://mlsanity.com/paper/2502.10721/) (2025)
- [Universal Time-Series Representation Learning: A Survey](https://mlsanity.com/paper/2401.03717/) (2024)
- [SETransformer: A Hybrid Attention-Based Architecture for Robust Human Activity Recognition](https://mlsanity.com/paper/2505.19369/) (2025)
- [Unified Spatial-Temporal Edge-Enhanced Graph Networks for Pedestrian Trajectory Prediction](https://mlsanity.com/paper/2502.02504/) (2025)
- [Revisiting Multivariate Time Series Forecasting with Missing Values](https://mlsanity.com/paper/2509.23494/) (2025)
- [ST-USleepNet: A Spatial-Temporal Coupling Prominence Network for Multi-Channel Sleep Staging](https://mlsanity.com/paper/2408.11884/) (2024)
- [Temporal Source Recovery for Time-Series Source-Free Unsupervised Domain Adaptation](https://mlsanity.com/paper/2409.19635/) (2024)
- [Graph Generation Powered with LLMs for Boosting Multivariate Time-Series Representation Learning](https://mlsanity.com/paper/2403.03645/) (2024)
- [A Survey on Graph Neural Networks for Remaining Useful Life Prediction: Methodologies, Evaluation and Future Trends](https://mlsanity.com/paper/2409.19629/) (2024)
- [MSA-CNN: A Lightweight Multi-Scale CNN with Attention for Sleep Stage Classification](https://mlsanity.com/paper/2501.02949/) (2025)
- [Routing Channel-Patch Dependencies in Time Series Forecasting with Graph Spectral Decomposition](https://mlsanity.com/paper/2603.13702/) (2026)
- [LEL: Lipschitz Continuity Constrained Ensemble Learning for Efficient EEG-Based Intra-subject Emotion Recognition](https://mlsanity.com/paper/2504.09156/) (2025)
- [ALCo-FM: Adaptive Long-Context Foundation Model for Accident Prediction](https://mlsanity.com/paper/2507.08153/) (2025)
- [Deep Domain Adaptation for Turbofan Engine Remaining Useful Life Prediction: Methodologies, Evaluation and Future Trends](https://mlsanity.com/paper/2510.03604/) (2025)
- [TimeFormer: Transformer with Attention Modulation Empowered by Temporal Characteristics for Time Series Forecasting](https://mlsanity.com/paper/2510.06680/) (2025)
- [Citywide Electric Vehicle Charging Demand Prediction Approach Considering Urban Region and Dynamic Influences](https://mlsanity.com/paper/2410.18766/) (2024)
- [Higher-order Cross-structural Embedding Model for Time Series Analysis](https://mlsanity.com/paper/2410.22984/) (2024)
- [Causal and Local Correlations Based Network for Multivariate Time Series Classification](https://mlsanity.com/paper/2411.18008/) (2024)
- [STRGCN: Capturing Asynchronous Spatio-Temporal Dependencies for Irregular Multivariate Time Series Forecasting](https://mlsanity.com/paper/2505.04167/) (2025)
- [PRISM: Lightweight Multivariate Time-Series Classification through Symmetric Multi-Resolution Convolutional Layers](https://mlsanity.com/paper/2508.04503/) (2025)
- [Ada-TransGNN: An Air Quality Prediction Model Based On Adaptive Graph Convolutional Networks](https://mlsanity.com/paper/2508.17867/) (2025)
- [Multivariate Time Series Forecasting with Hybrid Euclidean-SPD Manifold Graph Neural Networks](https://mlsanity.com/paper/2512.14023/) (2025)
- [CGSTA: Cross-Scale Graph Contrast with Stability-Aware Alignment for Multivariate Time-Series Anomaly Detection](https://mlsanity.com/paper/2602.20468/) (2026)

## Abstract (arXiv)

Multivariate Time-Series (MTS) data is crucial in various application fields. With its sequential and multi-source (multiple sensors) properties, MTS data inherently exhibits Spatial-Temporal (ST) dependencies, involving temporal correlations between timestamps and spatial correlations between sensors in each timestamp. To effectively leverage this information, Graph Neural Network-based methods (GNNs) have been widely adopted. However, existing approaches separately capture spatial dependency and temporal dependency and fail to capture the correlations between Different sEnsors at Different Timestamps (DEDT). Overlooking such correlations hinders the comprehensive modelling of ST dependencies within MTS data, thus restricting existing GNNs from learning effective representations. To address this limitation, we propose a novel method called Fully-Connected Spatial-Temporal Graph Neural Network (FC-STGNN), including two key components namely FC graph construction and FC graph convolution. For graph construction, we design a decay graph to connect sensors across all timestamps based on their temporal distances, enabling us to fully model the ST dependencies by considering the correlations between DEDT. Further, we devise FC graph convolution with a moving-pooling GNN layer to effectively capture the ST dependencies for learning effective representations. Extensive experiments show the effectiveness of FC-STGNN on multiple MTS datasets compared to SOTA methods. The code is available at https://github.com/Frank-Wang-oss/FCSTGNN.