# Regularized Graph Structure Learning with Semantic Knowledge for Multi-variates Time-Series Forecasting

arXiv: https://arxiv.org/abs/2210.06126 · HTML: https://mlsanity.com/paper/2210.06126/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 33 references that are in the map.
- First posted on arXiv 12 Oct 2022.

## Builds on (most cited first, 12 of 12)

- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [Adaptive Graph Convolutional Recurrent Network for Traffic Forecasting](https://mlsanity.com/paper/2007.02842/) (2020)
- [Spectral Temporal Graph Neural Network for Multivariate Time-series Forecasting](https://mlsanity.com/paper/2103.07719/) (2021)
- [Discrete Graph Structure Learning for Forecasting Multiple Time Series](https://mlsanity.com/paper/2101.06861/) (2021)
- [Z-GCNETs: Time Zigzags at Graph Convolutional Networks for Time Series Forecasting](https://mlsanity.com/paper/2105.04100/) (2021)
- [TSSRGCN: Temporal Spectral Spatial Retrieval Graph Convolutional Network for Traffic Flow Forecasting](https://mlsanity.com/paper/2011.14638/) (2020)
- [GoG: Relation-aware Graph-over-Graph Network for Visual Dialog](https://mlsanity.com/paper/2109.08475/) (2021)
- [Forecaster: A Graph Transformer for Forecasting Spatial and Time-Dependent Data](https://mlsanity.com/paper/1909.04019/) (2019)
- [Deep Multi-View Spatiotemporal Virtual Graph Neural Network for Significant Citywide Ride-hailing Demand Prediction](https://mlsanity.com/paper/2007.15189/) (2020)
- [Demand Forecasting from Spatiotemporal Data with Graph Networks and Temporal-Guided Embedding](https://mlsanity.com/paper/1905.10709/) (2019)

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

- [A Survey on Graph Neural Networks for Time Series: Forecasting, Classification, Imputation, and Anomaly Detection](https://mlsanity.com/paper/2307.03759/) (2023)
- [Graph Neural Networks for Tabular Data Learning: A Survey with Taxonomy and Directions](https://mlsanity.com/paper/2401.02143/) (2024)
- [STGC-GNNs: A GNN-based traffic prediction framework with a spatial-temporal Granger causality graph](https://mlsanity.com/paper/2210.16789/) (2022)
- [STG4Traffic: A Survey and Benchmark of Spatial-Temporal Graph Neural Networks for Traffic Prediction](https://mlsanity.com/paper/2307.00495/) (2023)
- [STS-CCL: Spatial-Temporal Synchronous Contextual Contrastive Learning for Urban Traffic Forecasting](https://mlsanity.com/paper/2307.02507/) (2023)
- [Vision HgNN: An Electron-Micrograph is Worth Hypergraph of Hypernodes](https://mlsanity.com/paper/2408.11351/) (2024)
- [DSTCGCN: Learning Dynamic Spatial-Temporal Cross Dependencies for Traffic Forecasting](https://mlsanity.com/paper/2307.00518/) (2023)
- [Dynamic Graph Convolutional Network with Attention Fusion for Traffic Flow Prediction](https://mlsanity.com/paper/2302.12598/) (2023)
- [SAMSGL: Series-Aligned Multi-Scale Graph Learning for Spatio-Temporal Forecasting](https://mlsanity.com/paper/2312.02646/) (2023)
- [Review of Data-centric Time Series Analysis from Sample, Feature, and Period](https://mlsanity.com/paper/2404.16886/) (2024)
- [Robust Multivariate Time Series Forecasting against Intra- and Inter-Series Transitional Shift](https://mlsanity.com/paper/2407.13194/) (2024)
- [SSMT: Few-Shot Traffic Forecasting with Single Source Meta-Transfer](https://mlsanity.com/paper/2410.15589/) (2024)
- [ADFormer: Aggregation Differential Transformer for Passenger Demand Forecasting](https://mlsanity.com/paper/2506.02576/) (2025)
- [Efficient Traffic Forecasting on Large-Scale Road Network by Regularized Adaptive Graph Convolution](https://mlsanity.com/paper/2506.07179/) (2025)
- [Beyond Pairwise Connections: Extracting High-Order Functional Brain Network Structures under Global Constraints](https://mlsanity.com/paper/2510.09175/) (2025)
- [Insider Threat Detection Using GCN and Bi-LSTM with Explicit and Implicit Graph Representations](https://mlsanity.com/paper/2512.18483/) (2025)
- [Sparsity exploitation via discovering graphical models in multi-variate time-series forecasting](https://mlsanity.com/paper/2306.17090/) (2023)
- [Multi-Scale Spatial-Temporal Recurrent Networks for Traffic Flow Prediction](https://mlsanity.com/paper/2310.08138/) (2023)
- [Global-Aware Enhanced Spatial-Temporal Graph Recurrent Networks: A New Framework For Traffic Flow Prediction](https://mlsanity.com/paper/2401.04135/) (2024)
- [From Chaos to Clarity: Time Series Anomaly Detection in Astronomical Observations](https://mlsanity.com/paper/2403.10220/) (2024)
- [MIXAD: Memory-Induced Explainable Time Series Anomaly Detection](https://mlsanity.com/paper/2410.22735/) (2024)
- [STAHGNet: Modeling Hybrid-grained Heterogenous Dependency Efficiently for Traffic Prediction](https://mlsanity.com/paper/2412.17524/) (2024)
- [DRAN: A Distribution and Relation Adaptive Network for Spatio-temporal Forecasting](https://mlsanity.com/paper/2504.01531/) (2025)

## Abstract (arXiv)

Multivariate time-series forecasting is a critical task for many applications, and graph time-series network is widely studied due to its capability to capture the spatial-temporal correlation simultaneously. However, most existing works focus more on learning with the explicit prior graph structure, while ignoring potential information from the implicit graph structure, yielding incomplete structure modeling. Some recent works attempt to learn the intrinsic or implicit graph structure directly while lacking a way to combine explicit prior structure with implicit structure together. In this paper, we propose Regularized Graph Structure Learning (RGSL) model to incorporate both explicit prior structure and implicit structure together, and learn the forecasting deep networks along with the graph structure. RGSL consists of two innovative modules. First, we derive an implicit dense similarity matrix through node embedding, and learn the sparse graph structure using the Regularized Graph Generation (RGG) based on the Gumbel Softmax trick. Second, we propose a Laplacian Matrix Mixed-up Module (LM3) to fuse the explicit graph and implicit graph together. We conduct experiments on three real-word datasets. Results show that the proposed RGSL model outperforms existing graph forecasting algorithms with a notable margin, while learning meaningful graph structure simultaneously. Our code and models are made publicly available at https://github.com/alipay/RGSL.git.