The unprecedented availability of traffic data and advances in data-driven algorithms have sparked considerable interest Deep learning-based multivariate and multistepahead and rapid developments in traffic forecasting. State-of-theart traffic forecasting models are typically deep learning models such as DCRNN (Li et al., 2017), trained with the mean squared error (MSE) or STGCN (Yu et al., 2017), Graph-Wavenet (Wu et al., 2019), mean absolute error (MAE) as the loss function in and Traffic Transformer (Cai et al., 2020), have demonstrated a sequence-to-sequence setting, simply assuming superior performance for traffic speed forecasting that the errors follow an independent and isotropic over classical methods. Deep neural networks have shown Gaussian or Laplacian distributions. However, clear advantages in capturing complex non-linear relationships such assumptions are often unrealistic for realworld in traffic forecasting; for example, in the aforementioned traffic forecasting tasks, where the probabilistic models, Graph Neural Networks (GNNs), Recurrent distribution of spatiotemporal forecasting Neural Networks (RNNs), Gated Convolutional Neural Networks is very complex with strong concurrent correlations (Gated-CNNs), and Transformers are employed to across both sensors and forecasting horizons capture those unique spatiotemporal patterns in traffic data in a time-varying manner.

Spatiotemporal traffic data imputation is of great significance in intelligent transportation systems and data-driven decision-making processes. To make an accurate reconstruction from partially observed traffic data, we assert the importance of characterizing both global and local trends in traffic time series. In the literature, substantial prior works have demonstrated the effectiveness of utilizing low-rankness 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 in the form of circular convolution. Then, we develop a low-rank Laplacian convolutional representation (LCR) model by putting the nuclear norm of a circulant matrix and the Laplacian temporal regularization together, which is proved to meet a unified framework that takes a fast Fourier transform (FFT) solution in a relatively low time complexity. Through extensive experiments on some traffic datasets, we demonstrate the superiority of LCR for imputing traffic time series of various time series behaviors (e.g., data noises and strong/weak periodicity). The proposed LCR model is an efficient and effective solution to large-scale traffic data imputation over the existing baseline models. Despite the LCR's application to time series data, the key modeling idea lies in bridging the low-rank models and the Laplacian regularization through FFT, which is also applicable to image inpainting. The adapted datasets and Python implementation are publicly available at https://github.com/xinychen/transdim.

The problem of broad practical interest in spatiotemporal data analysis, i.e., discovering interpretable dynamic patterns from spatiotemporal data, is studied in this paper. Towards this end, we develop a time-varying reduced-rank vector autoregression (VAR) model whose coefficient matrices are parameterized by low-rank tensor factorization. Benefiting from the tensor factorization structure, the proposed model can simultaneously achieve model compression and pattern discovery. In particular, the proposed model allows one to characterize nonstationarity and time-varying system behaviors underlying spatiotemporal data. To evaluate the proposed model, extensive experiments are conducted on various spatiotemporal data representing different nonlinear dynamical systems, including fluid dynamics, sea surface temperature, USA surface temperature, and NYC taxi trips. Experimental results demonstrate the effectiveness of modeling spatiotemporal data and characterizing spatial/temporal patterns with the proposed model. In the spatial context, the spatial patterns can be automatically extracted and intuitively characterized by the spatial modes. In the temporal context, the complex time-varying system behaviors can be revealed by the temporal modes in the proposed model. Thus, our model lays an insightful foundation for understanding complex spatiotemporal data in real-world dynamical systems. The adapted datasets and Python implementation are publicly available at https://github.com/xinychen/vars.

Modern time series datasets are often high-dimensional, incomplete/sparse, and nonstationary. These properties hinder the development of scalable and efficient solutions for time series forecasting and analysis. To address these challenges, we propose a Nonstationary Temporal Matrix Factorization (NoTMF) model, in which matrix factorization is used to reconstruct the whole time series matrix and vector autoregressive (VAR) process is imposed on a properly differenced copy of the temporal factor matrix. This approach not only preserves the low-rank property of the data but also offers consistent temporal dynamics. The learning process of NoTMF involves the optimization of two factor matrices and a collection of VAR coefficient matrices. To efficiently solve the optimization problem, we derive an alternating minimization framework, in which subproblems are solved using conjugate gradient and least squares methods. In particular, the use of conjugate gradient method offers an efficient routine and allows us to apply NoTMF on large-scale problems. Through extensive experiments on Uber movement speed dataset, we demonstrate the superior accuracy and effectiveness of NoTMF over other baseline models. Our results also confirm the importance of addressing the nonstationarity of real-world time series data such as spatiotemporal traffic flow/speed.

Advancements in Intelligent Traffic Systems (ITS) have made huge amounts of traffic data available through automatic data collection. A big part of this data is stored as trajectories of moving vehicles and road users. Automatic analysis of this data with minimal human supervision would both lower the costs and eliminate subjectivity of the analysis. Trajectory clustering is an unsupervised task. In this paper, we perform a comprehensive comparison of similarity measures, clustering algorithms and evaluation measures using trajectory data from seven intersections. We also propose a method to automatically generate trajectory reference clusters based on their origin and destination points to be used for label-based evaluation measures. Therefore, the entire procedure remains unsupervised both in clustering and evaluation levels. Finally, we use a combination of evaluation measures to find the top performing similarity measures and clustering algorithms for each intersection. The results show that there is no single combination of distance and clustering algorithm that is always among the top ten clustering setups.

We consider the problem of predicting the future path of a pedestrian using its motion history and the motion history of the surrounding pedestrians, called social information. Since the seminal paper on Social-LSTM, deep-learning has become the main tool used to model the impact of social interactions on a pedestrian's motion. The demonstration that these models can learn social interactions relies on an ablative study of these models. The models are compared with and without their social interactions module on two standard metrics, the Average Displacement Error and Final Displacement Error. Yet, these complex models were recently outperformed by a simple constant-velocity approach. This questions if they actually allow to model social interactions as well as the validity of the proof. In this paper, we focus on the deep-learning models with a soft-attention mechanism for social interaction modeling and study whether they use social information at prediction time. We conduct two experiments across four state-of-the-art approaches on the ETH and UCY datasets, which were also used in previous work. First, the models are trained by replacing the social information with random noise and compared to model trained with actual social information. Second, we use a gating mechanism along with a $L_0$ penalty, allowing models to shut down their inner components. The models consistently learn to prune their soft-attention mechanism. For both experiments, neither the course of the convergence nor the prediction performance were altered. This demonstrates that the soft-attention mechanism and therefore the social information are ignored by the models.

Spatiotemporal traffic time series (e.g., traffic volume/speed) collected from sensing systems are often incomplete with considerable corruption and large amounts of missing values, preventing users from harnessing the full power of the data. Missing data imputation has been a long-standing research topic and critical application for real-world intelligent transportation systems. A widely applied imputation method is low-rank matrix/tensor completion; however, the low-rank assumption only preserves the global structure while ignores the strong local consistency in spatiotemporal data. In this paper, we propose a low-rank autoregressive tensor completion (LATC) framework by introducing \textit{temporal variation} as a new regularization term into the completion of a third-order (sensor $\times$ time of day $\times$ day) tensor. The third-order tensor structure allows us to better capture the global consistency of traffic data, such as the inherent seasonality and day-to-day similarity. To achieve local consistency, we design the temporal variation by imposing an AR($p$) model for each time series with coefficients as learnable parameters. Different from previous spatial and temporal regularization schemes, the minimization of temporal variation can better characterize temporal generative mechanisms beyond local smoothness, allowing us to deal with more challenging scenarios such "blackout" missing. To solve the optimization problem in LATC, we introduce an alternating minimization scheme that estimates the low-rank tensor and autoregressive coefficients iteratively. We conduct extensive numerical experiments on several real-world traffic data sets, and our results demonstrate the effectiveness of LATC in diverse missing scenarios.

Intersections constitute one of the most dangerous elements in road systems. Traffic signals remain the most common way to control traffic at high-volume intersections and offer many opportunities to apply intelligent transportation systems to make traffic more efficient and safe. This paper describes an automated method to estimate the temporal exposure of road users crossing the conflict zone to lateral collision with road users originating from a different approach. This component is part of a larger system relying on video sensors to provide queue lengths and spatial occupancy that are used for real time traffic control and monitoring. The method is evaluated on data collected during a real world experiment.