# Laplacian Convolutional Representation for Traffic Time Series Imputation

arXiv: https://arxiv.org/abs/2212.01529 · HTML: https://mlsanity.com/paper/2212.01529/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 57 references that are in the map.
- First posted on arXiv 3 Dec 2022.

## Builds on (most cited first, 14 of 14)

- [The highD Dataset: A Drone Dataset of Naturalistic Vehicle Trajectories on German Highways for Validation of Highly Automated Driving Systems](https://mlsanity.com/paper/1810.05642/) (2018)
- [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)
- [Bayesian Temporal Factorization for Multidimensional Time Series Prediction](https://mlsanity.com/paper/1910.06366/) (2019)
- [CitySim: A Drone-Based Vehicle Trajectory Dataset for Safety Oriented Research and Digital Twins](https://mlsanity.com/paper/2208.11036/) (2022)
- [Low-Rank Autoregressive Tensor Completion for Spatiotemporal Traffic Data Imputation](https://mlsanity.com/paper/2104.14936/) (2021)
- [A Nonconvex Low-Rank Tensor Completion Model for Spatiotemporal Traffic Data Imputation](https://mlsanity.com/paper/2003.10271/) (2020)
- [Tensor-based formulation and nuclear norm regularization for multi-energy computed tomography](https://mlsanity.com/paper/1307.5348/) (2013)
- [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)
- [Scalable Low-Rank Tensor Learning for Spatiotemporal Traffic Data Imputation](https://mlsanity.com/paper/2008.03194/) (2020)
- [Time Series Forecasting via Learning Convolutionally Low-Rank Models](https://mlsanity.com/paper/2104.11510/) (2021)
- [Forecasting Sparse Movement Speed of Urban Road Networks with Nonstationary Temporal Matrix Factorization](https://mlsanity.com/paper/2203.10651/) (2022)

## Built on by (most cited first, 18 of 18)

- [ImputeFormer: Low Rankness-Induced Transformers for Generalizable Spatiotemporal Imputation](https://mlsanity.com/paper/2312.01728/) (2023)
- [Merlin: Multi-View Representation Learning for Robust Multivariate Time Series Forecasting with Unfixed Missing Rates](https://mlsanity.com/paper/2506.12459/) (2025)
- [Spatiotemporal Implicit Neural Representation as a Generalized Traffic Data Learner](https://mlsanity.com/paper/2405.03185/) (2024)
- [ODMixer: Fine-grained Spatial-temporal MLP for Metro Origin-Destination Prediction](https://mlsanity.com/paper/2404.15734/) (2024)
- [Accelerating Ill-conditioned Hankel Matrix Recovery via Structured Newton-like Descent](https://mlsanity.com/paper/2406.07409/) (2024)
- [Correlating Time Series with Interpretable Convolutional Kernels](https://mlsanity.com/paper/2409.01362/) (2024)
- [Guaranteed Multidimensional Time Series Prediction via Deterministic Tensor Completion Theory](https://mlsanity.com/paper/2501.15388/) (2025)
- [FADTI: Fourier and Attention Driven Diffusion for Multivariate Time Series Imputation](https://mlsanity.com/paper/2512.15116/) (2025)
- [Graph Signal Adaptive Message Passing](https://mlsanity.com/paper/2410.17629/) (2024)
- [Spatial-Temporal Feedback Diffusion Guidance for Controlled Traffic Imputation](https://mlsanity.com/paper/2601.04572/) (2026)
- [Learning Higher-Order Interactions from Incomplete Spatiotemporal Data with Mixtures of Hypergraph Laplacians](https://mlsanity.com/paper/2605.17316/) (2026)
- [A Survey and Benchmarking of Spatial-Temporal Traffic Data Imputation Models](https://mlsanity.com/paper/2412.04733/) (2024)
- [Collaborative Imputation of Urban Time Series through Cross-city Meta-learning](https://mlsanity.com/paper/2501.11306/) (2025)
- [Property Inheritance for Subtensors in Tensor Train Decompositions](https://mlsanity.com/paper/2504.11396/) (2025)
- [Robust Tensor Completion via Gradient Tensor Nulclear L1-L2 Norm for Traffic Data Recovery](https://mlsanity.com/paper/2506.22732/) (2025)
- [A Spatio-Temporal Online Robust Tensor Recovery Approach for Streaming Traffic Data Imputation](https://mlsanity.com/paper/2511.01267/) (2025)
- [Exact Recovery of Non-Random Missing Multidimensional Time Series via Temporal Isometric Delay-Embedding Transform](https://mlsanity.com/paper/2512.10191/) (2025)
- [A Multi-View Coupled Tensor Decomposition for Lightweight Online Adaptive Traffic Prediction](https://mlsanity.com/paper/2608.25498/) (2026)

## Abstract (arXiv)

Spatiotemporal traffic data imputation is of great significance in intelligent transportation systems and data-driven decision-making processes. To perform efficient learning and accurate reconstruction from partially observed traffic data, we assert the importance of characterizing both global and local trends in time series. In the literature, substantial works have demonstrated the effectiveness of utilizing the low-rank property of traffic data by matrix/tensor completion models. In this study, we first introduce a Laplacian kernel to temporal regularization for characterizing local trends in traffic time series, which can be formulated as a circular convolution. Then, we develop a low-rank Laplacian convolutional representation (LCR) model by putting the circulant matrix nuclear norm and the Laplacian kernelized temporal regularization together, which is proved to meet a unified framework that has a fast Fourier transform (FFT) solution in log-linear time complexity. Through extensive experiments on several traffic datasets, we demonstrate the superiority of LCR over several baseline models for imputing traffic time series of various time series behaviors (e.g., data noises and strong/weak periodicity) and reconstructing sparse speed fields of vehicular traffic flow. The proposed LCR model is also an efficient solution to large-scale traffic data imputation over the existing imputation models.