A Multi-View Coupled Tensor Decomposition for Lightweight Online Adaptive Traffic Prediction

Quan Yu; Jie Ni; Yu-Hong Dai; Xiongjun Zhang

math.OCAug 26, 2026

A Multi-View Coupled Tensor Decomposition for Lightweight Online Adaptive Traffic Prediction

Authors: Quan Yu, Jie Ni, Yu-Hong Dai, Xiongjun Zhang

Organizations: School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China, and also with the Key Laboratory of Nonlinear Analysis and Applications (Ministry of Education), Central China Normal University · School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China · State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China, and also with the School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China · School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

Abstract

Accurate online traffic prediction is essential for intelligent transportation systems, where forecasting must be performed continuously under imperfect sensing conditions. Missing observations and anomalous disturbances make this task challenging, particularly when prediction relies on a single traffic view. This paper proposes a Multi-View Coupled Tensor Decomposition (MVCTD) model for online traffic prediction from imperfect multi-view observations, such as speed, flow, and occupancy. The proposed model uses coupled tensor decomposition to build a structured latent forecasting space, in which shared spatial structures across traffic views and view-specific temporal dynamics are jointly modeled. A group sparse regularization is further introduced to capture correlated abnormal responses induced by real traffic anomalies and thus reduce their influence on forecasts. For streaming deployment, MVCTD performs iterative refinement only on the current latent tensor, while the remaining model variables are updated by lightweight closed-form steps based on summarized historical information, thereby avoiding repeated optimization over the full historical sequence. Experiments on real-world traffic datasets demonstrate that MVCTD achieves accurate forecasts with favorable runtime under severe missingness, confirming its suitability for online traffic prediction.

Figures & tables

Panel of Figure 1 — Fig. 1 : Schematic illustration of rolling online traffic forecasting with incomplete observations.

Panel of Figure 2 — Fig. 2 : The proposed MVCTD framework.

\left\{\begin{array}[]{l}\mathcal{P}_{d}^{k+1}=\mathcal{P}_{d}^{k}+\eta_{1}^{k}(\mathcal{A}^{k+1}*\mathcal{Z}_{d}^{k+1}+\mathcal{E}_{d}^{k+1}-\mathcal{X}_{d}^{k+1});\\ \mathcal{Q}_{d}^{k+1}=\mathcal{Q}_{d}^{k}+\eta_{2}^{k}(\mathcal{Y}_{d}^{k+1}-\mathcal{Z}_{d}^{k+1});\\ \mathcal{R}_{d}^{k+1}=\mathcal{R}_{d}^{k}+\eta_{3}^{k}(\mathcal{C}_{d}^{k+1}-\mathcal{Z}_{d}^{k+1});\\ \eta_{i}^{k+1}=\beta\eta_{i}^{k},i\in[3].\end{array}\right.

(23)

Algorithm 1 Stage I: Offline Initialization via Batch ADMM.

Dataset	Method	MAPE			RMSE			Time (s)
Dataset	Method	Volume	Occupancy	Speed	Volume	Occupancy	Speed	Time (s)
PeMS-D4	MVCTD	14.42	17.91	5.24	36.18	2.46	4.83	101
	HTMF	32.41	59.13	6.80	55.13	3.00	5.54	4384
	BTMF	36.52	64.11	7.43	67.78	3.31	5.99	663
	circDMDsp	36.44	50.33	8.10	62.70	3.22	7.50	425
	PatchTST	50.34	59.21	8.37	68.50	3.45	7.01	2686

TABLE I : Comparison of forecasting performance with full observations.

Dataset	Method	MAPE			RMSE			Time (s)
Dataset	Method	Volume	Occupancy	Speed	Volume	Occupancy	Speed	Time (s)
PeMS-D4	MVCTD	15.48	18.71	5.81	38.60	2.55	5.16	72
	HTMF	35.68	52.79	7.18	58.62	2.94	5.68	2501
	BTMF	36.59	65.04	7.60	69.45	3.33	6.07	1871
PeMS-D8	MVCTD	12.15	13.81	4.49	38.87	2.29	4.50	38
	HTMF	27.46	37.09	6.28	57.33	3.83	5.19	3629

TABLE II : Comparison of forecasting performance under 80% missing rate.

Fig. 3 : Time series prediction of average traffic volume on the PeMS-D8 dataset with full observations.

Panel of Figure 7 — Fig. 4 : Parameter analysis of MVCTD with respect to $\lambda_{i}$ and $\gamma$ on the PeMS-D8 dataset under 40% missing rate.

Method	MAPE			RMSE
Method	Volume	Occupancy	Speed	Volume	Occupancy	Speed
w/o Anomaly	22.94	42.25	5.48	52.74	3.71	5.54
w/o Global Periodicity	12.22	14.22	3.98	38.00	2.25	4.29
w/o Local Smoothness	11.61	14.07	3.97	37.85	2.27	4.28
Proposed	11.31	13.26	3.94	37.50	2.25	4.24

TABLE III : Ablation study of different regularization terms on the PeMS-D8 dataset under 40% missing rate.

Datasets	Strategy	MAPE (%)			RMSE
Datasets	Strategy	Volume	Occupancy	Speed	Volume	Occupancy	Speed
PeMS-D4	Single-View	15.92	19.87	6.02	37.86	2.61	5.37
PeMS-D4	Proposed	15.48	18.71	5.81	38.60	2.55	5.16
PeMS-D8	Single-View	12.24	14.03	4.67	39.17	2.40	4.75
PeMS-D8	Proposed	12.15	13.81	4.49	38.87	2.29	4.50

TABLE IV : Performance comparison between single-view and multi-view modeling strategies.

Time Lag Set	MAPE			RMSE
Time Lag Set	Volume	Occupancy	Speed	Volume	Occupancy	Speed
$\{1\}$	22.74	26.77	5.62	60.62	3.03	5.44
$\{1,\dots,7\}$	12.32	14.56	4.18	37.15	2.28	4.33
Proposed	11.31	13.26	3.94	37.50	2.25	4.24

TABLE V : Impact of different autoregressive lag structures on prediction performance.

Panel of Figure 11 — Fig. 5 : Convergence curves of Algorithm 1 on the PeMS-D8 dataset under different Missing Rates (MR).

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Traffic forecasting predicts future flows, speeds, demand, travel times, and congestion from spatial, temporal, and contextual data.

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Feb 25, 2026J/K move · Enter open · S save

Learning from Yesterday's Error: An Efficient Online Learning Method for Traffic Demand Prediction

Xiannan Huang, Quan Yuan, Chao Yang

Key Laboratory of Road and Traffic Engineering, Ministry of Education at Tongji University, 4800 Cao’an Road, Shanghai, 201804, Shanghai, China · Urban Mobility Institute, Tongji University, 1239 Siping Road, Shanghai, 200092, Shanghai, China

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Accurately predicting short-term traffic demand is critical for intelligent transportation systems. While deep learning models achieve strong performance under stationary conditions, their accuracy often degrades significantly when faced with distribution shifts caused by external events or evolving urban dynamics. Frequent model retraining to adapt to such changes incurs prohibitive computational costs, especially for large-scale or foundation models. To address this challenge, we propose FORESEE (Forecasting Online with Residual Smoothing and Ensemble Experts), a lightweight online adaptation framework that is accurate, robust, and computationally efficient. FORESEE operates without any parameter updates to the base model. Instead, it corrects today's forecast in each region using yesterday's prediction error, stabilized through exponential smoothing guided by a mixture-of-experts mechanism that adapts to recent error dynamics. Moreover, an adaptive spatiotemporal smoothing component propagates error signals across neighboring regions and time slots, capturing coherent shifts in demand patterns. Extensive experiments on seven real-world datasets with three backbone models demonstrate that FORESEE consistently improves prediction accuracy, maintains robustness even when distribution shifts are minimal (avoiding performance degradation), and achieves the lowest computational overhead among existing online methods. By enabling real-time adaptation of traffic forecasting models with negligible computational cost, FORESEE paves the way for deploying reliable, up-to-date prediction systems in dynamic urban environments. Code and data are available at https://github.com/xiannanhuang/FORESEE

Abstract

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