Spatio-Temporal Partial Sensing Forecast for Long-term Traffic

Zibo Liu; Zhe Jiang; Zelin Xu; Tingsong Xiao; Zhengkun Xiao; Yupu zhang; Haibo Wang; Shigang Chen

cs.LGAug 2, 2024

Spatio-Temporal Partial Sensing Forecast for Long-term Traffic

Authors: Zibo Liu, Zhe Jiang, Zelin Xu, Tingsong Xiao, Zhengkun Xiao, Yupu zhang, Haibo Wang, Shigang Chen

Organizations: Department of Computer & Information Science & Engineering, University of Florida · Department of Computer Science, University of Kentucky

Abstract

Traffic forecasting uses recent measurements by sensors installed at chosen locations to forecast the future road traffic. Existing work either assumes all locations are equipped with sensors or focuses on short-term forecast. This paper studies partial sensing forecast of long-term traffic, assuming sensors are available only at some locations. The problem is challenging due to the unknown data distribution at unsensed locations, the intricate spatio-temporal correlation in long-term forecasting, as well as noise to traffic patterns. We propose a Spatio-temporal Long-term Partial sensing Forecast model (SLPF) for traffic prediction, with several novel contributions, including a rank-based embedding technique to reduce the impact of noise in data, a spatial transfer matrix to overcome the spatial distribution shift from sensed locations to unsensed locations, and a multi-step training process that utilizes all available data to successively refine the model parameters for better accuracy. Extensive experiments on several real-world traffic datasets demonstrate its superior performance. Our source code is at https://github.com/zbliu98/SLPF

Figures & tables

Figure 1: Flow rates of three locations for two days

Figure 2: Noise has the greatest impact on GinAR for long-term partial sensing than for long-term full sensing, which is in turn more sensitive to noise than traditional short-term full sensing.

Figure 3: The model training phase consists of three steps above. After the model is trained and deployed, only $\mathcal{X}_{M,T}$ is collected for input, and $\mathcal{X}_{M^{\prime},T^{\prime}}$ is output.

Dataset	PEMS03	PEMS04	PEMS08	PEMS-BAY	METR-LA
Area	in CA, USA
Time Span	9/1/2018 -	1/1/2018 -	7/1/2016 -	1/1/2017 -	3/1/2012 -
	11/30/2018	2/28/2018	8/31/2016	5/31/2017	6/30/2012
Time Interval	5 min
Number of Locations, $n$	358	307	170	325	207
Number of Time Intervals	26,208	16,992	17,856	52,116	34,272

Table 1: Basic statistics of the datasets used in our experiments.

Models	PEMS03			PEMS04			PEMS08			PEMSBAY			METRLA
	$m^{\prime}=250,m^{\prime}/n=69\%$			$m^{\prime}=250,m^{\prime}/n=81\%$			$m^{\prime}=150,m^{\prime}/n=88.2\%$			$m^{\prime}=250,m^{\prime}/n=76.9\%$			$m^{\prime}=150,m^{\prime}/n=72.4\%$
	MAE	RMSE	MAPE	MAE	RMSE	MAPE	MAE	RMSE	MAPE	MAE	RMSE	MAPE	MAE	RMSE	MAPE
Matrix Factorization ( Lee and Seung, 2000 )	69.01	110.17	135.41	91.38	150.09	129.65	76.01	132.64	85.13	6.25	15.63	20.21	16.72	34.21	49.83
PatchTST* ( Nie et al., 2022 )	57.71	86.33	103.23	58.28	86.15	54.99	43.90	64.68	28.59	4.58	8.66	12.50	11.67	21.81	26.86
iTransformer* ( Liu et al., 2023b )	67.31	103.07	127.88	87.44	125.04	99.1	69.81	91.03	61.24	5.13	9.60	15.62	13.65	22.58	27.51
D2STGNN* ( Shao et al., 2022c )	37.31	61.1	45.69	47.29	75.41	48.98	47.37	67.4	35.2	6.62	10.94	15.52	14.93	27.25	42.33

Table 2: Performance comparison over five datasets, where

n

is the total number of locations and

m^{\prime}

is the number of unsensed locations. A baseline model with suffix * is the model adapted for the partial sensing task. Our models are in bold at the bottom.

Method	MAE	RMSE	MAPE
SLPF	16.58	29.22	17.85
LPF (1 step, see Fig. 3 , from $\mathcal{X}_{M,T}$ to $\mathcal{X}_{M^{\prime},T^{\prime}}$ )	18.47	32.08	18.83
2 Step (from $\mathcal{X}_{M,T}$ to $\mathcal{X}_{M^{\prime},T}$ , then from $\mathcal{X}_{M,T}$ , $\mathcal{X}_{M^{\prime},T}$ to $\mathcal{X}_{M^{\prime},T^{\prime}}$ )	17.24	30.18	18.06
Plain Spatial Transfer Matrix	17.80	32.35	17.87
No Spatial Transfer Matrix	17.76	32.35	17.85
No Rank-based Node Embedding	17.39	31.95	17.89

Table 3: Different ablation methods under weighted selection and

m^{\prime}=50

condition on PEMS08 dataset over the average horizon.

Figure 4: Visualization on different locations when our model with or without ranking embedding.

Figure 5: Performance comparison with varying

\gamma

under Gaussian noise on PEMS08 dataset.

Figure 6: Performance comparison with varying

\gamma

under Uniform noise on PEMS08 dataset.

Figure 7: Performance comparison with varying

\gamma

under Laplace noise on PEMS08 dataset.

Figure 8: Comparing our model SLPF with the baselines in training efficient, in the context of accuracy-efficiency tradeoff, on dataset PEMS08, with weighted selection and

m^{\prime}=50

Figure 9: Improvement of SLPF over its variant without rank in bins of 5% forecasts with descending MAE, on dataset PEMS08 dataset with weighted selection and $m^{\prime}=50$ .

Figure 10: Accuracy comparison in terms of RMSE with respect to the number of unsensed locations under different selection methods on PEMS08 dataset.

Models	PEMS08
	MAE	RMSE	MAPE
STID ( Shao et al., 2022a )	19.59	32.20	13.05
PDFormer ( Jiang et al., 2023a )	18.58	31.86	12.64
STAEFormer ( Liu et al., 2023a )	18.77	32.73	12.10
TESTAM ( Lee and Ko, 2024 )	18.90	32.81	12.45
MegaCRN ( Jiang et al., 2023b )	19.99	33.67	13.09

Table 4: Performance comparison on PEMS08 dataset among the full-sensing baselines with the hypothetical assumption that they have the knowledge of the unsensed locations. The best results are in bold.

Figure 11: Accuracy comparison in terms of RMSE with respect to different forecasting lengths on PEMS08 dataset with the random selection method and the number of unsensed location being $m^{\prime}=50$ .

Figure 12: Impact of number of unsensed locations on forecast accuracy (RMSE) of SLPF when it is with or without rank-based node embedding, on PEMS08 dataset with weighted selection.

Figure 13: Parameter sensitivity of the proposed SLPF on the average horizon of PEMS08 with weighted selection and $m^{\prime}=150$ .

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Spatio-temporal traffic forecasting is a core component of intelligent transportation systems, supporting various downstream tasks such as signal control and network-level traffic management. In real-world deployments, forecasting models must operate under structural and observational uncertainties, conditions that are rarely considered in model design. Recent approaches achieve strong short-term predictive performance by tightly coupling spatial and temporal modeling, often at the cost of increased complexity and limited modularity. In contrast, efficient time-series models capture long-range temporal dependencies without relying on explicit network structure. We propose UniST-Pred, a unified spatio-temporal forecasting framework that first decouples temporal modeling from spatial representation learning, then integrates both through adaptive representation-level fusion. To assess robustness of the proposed approach, we construct a dataset based on an agent-based, microscopic traffic simulator (MATSim) and evaluate UniST-Pred under severe network disconnection scenarios. Additionally, we benchmark UniST-Pred on standard traffic prediction datasets, demonstrating its competitive performance against existing well-established models despite a lightweight design. The results illustrate that UniST-Pred maintains strong predictive performance across both real-world and simulated datasets, while also yielding interpretable spatio-temporal representations under infrastructure disruptions. The source code and the generated dataset are available at https://anonymous.4open.science/r/UniST-Pred-EF27

Abstract

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