A Double-Norm Aggregated Tensor Latent Factorization Model for Temporal-Aware Traffic Speed Imputation

TL;DR

TATSI tackles missing traffic speed data in ITS by blending robust $SL_1$-norm with traditional $L_2$-norm loss in a nonnegative tensor factorization framework. It uses a CP decomposition with latent factors for sensors, days, and times, and optimizes a joint objective that combines the two norms and a Frobenius regularization on the factors. The core contribution is the SLF-NMU solver, which updates the nonnegative factor matrices via multiplicative rules under a piecewise $SL_1$-norm regime, ensuring robustness to outliers while maintaining stability. Empirical results on three real-world traffic speed datasets show that TATSI achieves superior imputation accuracy (lower RMSE and MAE) across varying training data proportions, outperforming several baselines. The work highlights the practical impact of a double-norm approach for high-dimensional incomplete traffic data and points to future work on adaptive tuning of the regularization parameter $\ au$.

Abstract

In intelligent transportation systems (ITS), traffic management departments rely on sensors, cameras, and GPS devices to collect real-time traffic data. Traffic speed data is often incomplete due to sensor failures, data transmission delays, or occlusions, resulting in missing speed data in certain road segments. Currently, tensor decomposition based methods are extensively utilized, they mostly rely on the $L_2$-norm to construct their learning objectives, which leads to reduced robustness in the algorithms. To address this, we propose Temporal-Aware Traffic Speed Imputation (TATSI), which combines the $L_2$-norm and smooth $L_1$ (${SL}_1$)-norm in its loss function, thereby achieving both high accuracy and robust performance in imputing missing time-varying traffic speed data. TATSI adopts a single latent factor-dependent, nonnegative, and multiplicative update (SLF-NMU) approach, which serves as an efficient solver for performing nonnegative latent factor analysis (LFA) on a tensor. Empirical studies on three real-world time-varying traffic speed datasets demonstrate that, compared with state-of-the-art traffic speed predictors, TATSI more precisely captures temporal patterns, thereby yielding the most accurate imputations for missing traffic speed data.

Figures (3)

• Figure 1: An example of the speed sensor-day-time tensor for traffic.
• Figure 2: RMSE and MAE on the 10% training set
• Figure 3: RMSE and MAE on the 20% training set