# Correlating sparse sensing for large-scale traffic speed estimation: A Laplacian-enhanced low-rank tensor kriging approach

arXiv: https://arxiv.org/abs/2210.11780 · HTML: https://mlsanity.com/paper/2210.11780/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 60 references that are in the map.
- First posted on arXiv 21 Oct 2022.

## Builds on (most cited first, 22 of 22)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph WaveNet for Deep Spatial-Temporal Graph Modeling](https://mlsanity.com/paper/1906.00121/) (2019)
- [Revisiting Graph Neural Networks: All We Have is Low-Pass Filters](https://mlsanity.com/paper/1905.09550/) (2019)
- [GRAND: Graph Neural Diffusion](https://mlsanity.com/paper/2106.10934/) (2021)
- [Tensor Robust Principal Component Analysis with A New Tensor Nuclear Norm](https://mlsanity.com/paper/1804.03728/) (2018)
- [Inductive Graph Neural Networks for Spatiotemporal Kriging](https://mlsanity.com/paper/2006.07527/) (2020)
- [Graph Convolutional Networks using Heat Kernel for Semi-supervised Learning](https://mlsanity.com/paper/2007.16002/) (2020)
- [Tensor Robust Principal Component Analysis: Exact Recovery of Corrupted Low-Rank Tensors via Convex Optimization](https://mlsanity.com/paper/1708.04181/) (2017)
- [Low-Rank Autoregressive Tensor Completion for Spatiotemporal Traffic Data Imputation](https://mlsanity.com/paper/2104.14936/) (2021)
- [Tensor Completion for Weakly-dependent Data on Graph for Metro Passenger Flow Prediction](https://mlsanity.com/paper/1912.05693/) (2019)
- [Spatial Aggregation and Temporal Convolution Networks for Real-time Kriging](https://mlsanity.com/paper/2109.12144/) (2021)
- [Matrix Completion on Graphs](https://mlsanity.com/paper/1408.1717/) (2014)
- [Low-Rank Hankel Tensor Completion for Traffic Speed Estimation](https://mlsanity.com/paper/2105.11335/) (2021)
- [Missing Slice Recovery for Tensors Using a Low-rank Model in Embedded Space](https://mlsanity.com/paper/1804.01736/) (2018)
- [Recovery of Future Data via Convolution Nuclear Norm Minimization](https://mlsanity.com/paper/1909.03889/) (2019)
- [Block Hankel Tensor ARIMA for Multiple Short Time Series Forecasting](https://mlsanity.com/paper/2002.12135/) (2020)
- [Scalable Low-Rank Tensor Learning for Spatiotemporal Traffic Data Imputation](https://mlsanity.com/paper/2008.03194/) (2020)
- [Fast Low-Rank Bayesian Matrix Completion with Hierarchical Gaussian Prior Models](https://mlsanity.com/paper/1708.02455/) (2017)
- [Truncated tensor Schatten p-norm based approach for spatiotemporal traffic data imputation with complicated missing patterns](https://mlsanity.com/paper/2205.09390/) (2022)
- [Scalable Probabilistic Matrix Factorization with Graph-Based Priors](https://mlsanity.com/paper/1908.09393/) (2019)
- [Hankel-structured Tensor Robust PCA for Multivariate Traffic Time Series Anomaly Detection](https://mlsanity.com/paper/2110.04352/) (2021)
- [Bayesian Low-rank Matrix Completion with Dual-graph Embedding: Prior Analysis and Tuning-free Inference](https://mlsanity.com/paper/2203.10044/) (2022)

## Built on by (most cited first, 17 of 17)

- [ImputeFormer: Low Rankness-Induced Transformers for Generalizable Spatiotemporal Imputation](https://mlsanity.com/paper/2312.01728/) (2023)
- [Channel-Aware Low-Rank Adaptation in Time Series Forecasting](https://mlsanity.com/paper/2407.17246/) (2024)
- [Towards better traffic volume estimation: Jointly addressing the underdetermination and nonequilibrium problems with correlation-adaptive GNNs](https://mlsanity.com/paper/2303.05660/) (2023)
- [Spatiotemporal Implicit Neural Representation as a Generalized Traffic Data Learner](https://mlsanity.com/paper/2405.03185/) (2024)
- [Joint Estimation and Prediction of City-wide Delivery Demand: A Large Language Model Empowered Graph-based Learning Approach](https://mlsanity.com/paper/2408.17258/) (2024)
- [Network-wide Freeway Traffic Estimation Using Sparse Sensor Data: A Dirichlet Graph Auto-Encoder Approach](https://mlsanity.com/paper/2503.15845/) (2025)
- [Contextualizing MLP-Mixers Spatiotemporally for Urban Data Forecast at Scale](https://mlsanity.com/paper/2307.01482/) (2023)
- [Privacy-Preserving Data Fusion for Traffic State Estimation: A Vertical Federated Learning Approach](https://mlsanity.com/paper/2401.11836/) (2024)
- [MoGERNN: An Inductive Traffic Predictor for Unobserved Locations](https://mlsanity.com/paper/2501.12281/) (2025)
- [Traffic estimation in unobserved network locations using data-driven macroscopic models](https://mlsanity.com/paper/2401.17095/) (2024)
- [Spatial-Temporal Attention Model for Traffic State Estimation with Sparse Internet of Vehicles](https://mlsanity.com/paper/2407.08047/) (2024)
- [High-Dimensional Fault Tolerance Testing of Highly Automated Vehicles Based on Low-Rank Models](https://mlsanity.com/paper/2407.21069/) (2024)
- [Learning Higher-Order Interactions from Incomplete Spatiotemporal Data with Mixtures of Hypergraph Laplacians](https://mlsanity.com/paper/2605.17316/) (2026)
- [Tensor Completion Leveraging Graph Information: A Dynamic Regularization Approach with Statistical Guarantees](https://mlsanity.com/paper/2310.02543/) (2023)
- [MNT-TNN: Spatiotemporal Traffic Data Imputation via Compact Multimode Nonlinear Transform-based Tensor Nuclear Norm](https://mlsanity.com/paper/2503.22955/) (2025)
- [Robust Tensor Completion via Gradient Tensor Nulclear L1-L2 Norm for Traffic Data Recovery](https://mlsanity.com/paper/2506.22732/) (2025)
- [Metropolis-Scale Resilient and Trustworthy Traffic Flow Inference Using Multi-Source Data](https://mlsanity.com/paper/2605.25004/) (2026)

## Abstract (arXiv)

Traffic speed is central to characterizing the fluidity of the road network. Many transportation applications rely on it, such as real-time navigation, dynamic route planning, and congestion management. Rapid advances in sensing and communication techniques make traffic speed detection easier than ever. However, due to sparse deployment of static sensors or low penetration of mobile sensors, speeds detected are incomplete and far from network-wide use. In addition, sensors are prone to error or missing data due to various kinds of reasons, speeds from these sensors can become highly noisy. These drawbacks call for effective techniques to recover credible estimates from the incomplete data. In this work, we first identify the issue as a spatiotemporal kriging problem and propose a Laplacian enhanced low-rank tensor completion (LETC) framework featuring both lowrankness and multi-dimensional correlations for large-scale traffic speed kriging under limited observations. To be specific, three types of speed correlation including temporal continuity, temporal periodicity, and spatial proximity are carefully chosen and simultaneously modeled by three different forms of graph Laplacian, named temporal graph Fourier transform, generalized temporal consistency regularization, and diffusion graph regularization. We then design an efficient solution algorithm via several effective numeric techniques to scale up the proposed model to network-wide kriging. By performing experiments on two public million-level traffic speed datasets, we finally draw the conclusion and find our proposed LETC achieves the state-of-the-art kriging performance even under low observation rates, while at the same time saving more than half computing time compared with baseline methods. Some insights into spatiotemporal traffic data modeling and kriging at the network level are provided as well.