Correlating sparse sensing for large-scale traffic speed estimation: A Laplacian-enhanced low-rank tensor kriging approach

Traffic speed is central to characterizing the fluidity of the road network. Many transportation applications rely on it, such as real-time navigation, dynamic route planning, and congestion management. Rapid advances in sensing and communication techniques make traffic speed detection easier than ever. However, due to sparse deployment of static sensors or low penetration of mobile sensors, speeds detected are incomplete and far from network-wide use. In addition, sensors are prone to error or missing data due to various kinds of reasons, speeds from these sensors can become highly noisy. These drawbacks call for effective techniques to recover credible estimates from the incomplete data. In this work, we first identify the issue as a spatiotemporal kriging problem and propose a Laplacian enhanced low-rank tensor completion (LETC) framework featuring both lowrankness and multi-dimensional correlations for large-scale traffic speed kriging under limited observations. To be specific, three types of speed correlation including temporal continuity, temporal periodicity, and spatial proximity are carefully chosen and simultaneously modeled by three different forms of graph Laplacian, named temporal graph Fourier transform, generalized temporal consistency regularization, and diffusion graph regularization. We then design an efficient solution algorithm via several effective numeric techniques to scale up the proposed model to network-wide kriging. By performing experiments on two public million-level traffic speed datasets, we finally draw the conclusion and find our proposed LETC achieves the state-of-the-art kriging performance even under low observation rates, while at the same time saving more than half computing time compared with baseline methods. Some insights into spatiotemporal traffic data modeling and kriging at the network level are provided as well

Spatiotemporal Tensor Completion for Improved Urban Traffic Imputation

Effective management of urban traffic is important for any smart city initiative. Therefore, the quality of the sensory traffic data is of paramount importance. However, like any sensory data, urban traffic data are prone to imperfections leading to missing measurements. In this paper, we focus on inter-region traffic data completion. We model the inter-region traffic as a spatiotemporal tensor that suffers from missing measurements. To recover the missing data, we propose an enhanced CANDECOMP/PARAFAC (CP) completion approach that considers the urban and temporal aspects of the traffic. To derive the urban characteristics, we divide the area of study into regions. Then, for each region, we compute urban feature vectors inspired from biodiversity which are used to compute the urban similarity matrix. To mine the temporal aspect, we first conduct an entropy analysis to determine the most regular time-series. Then, we conduct a joint Fourier and correlation analysis to compute its periodicity and construct the temporal matrix. Both urban and temporal matrices are fed into a modified CP-completion objective function. To solve this objective, we propose an alternating least square approach that operates on the vectorized version of the inputs. We conduct comprehensive comparative study with two evaluation scenarios. In the first one, we simulate random missing values. In the second scenario, we simulate missing values at a given area and time duration. Our results demonstrate that our approach provides effective recovering performance reaching 26% improvement compared to state-of-art CP approaches and 35% compared to state-of-art generative model-based approaches

Tensor Completion for Weakly-dependent Data on Graph for Metro Passenger Flow Prediction

Low-rank tensor decomposition and completion have attracted significant interest from academia given the ubiquity of tensor data. However, the low-rank structure is a global property, which will not be fulfilled when the data presents complex and weak dependencies given specific graph structures. One particular application that motivates this study is the spatiotemporal data analysis. As shown in the preliminary study, weakly dependencies can worsen the low-rank tensor completion performance. In this paper, we propose a novel low-rank CANDECOMP / PARAFAC (CP) tensor decomposition and completion framework by introducing the $L_{1}$-norm penalty and Graph Laplacian penalty to model the weakly dependency on graph. We further propose an efficient optimization algorithm based on the Block Coordinate Descent for efficient estimation. A case study based on the metro passenger flow data in Hong Kong is conducted to demonstrate improved performance over the regular tensor completion methods.Comment: Accepted at AAAI 202

Multi-way Graph Signal Processing on Tensors: Integrative analysis of irregular geometries

Graph signal processing (GSP) is an important methodology for studying data residing on irregular structures. As acquired data is increasingly taking the form of multi-way tensors, new signal processing tools are needed to maximally utilize the multi-way structure within the data. In this paper, we review modern signal processing frameworks generalizing GSP to multi-way data, starting from graph signals coupled to familiar regular axes such as time in sensor networks, and then extending to general graphs across all tensor modes. This widely applicable paradigm motivates reformulating and improving upon classical problems and approaches to creatively address the challenges in tensor-based data. We synthesize common themes arising from current efforts to combine GSP with tensor analysis and highlight future directions in extending GSP to the multi-way paradigm.Comment: In review for IEEE Signal Processing Magazin

A Data Fusion CANDECOMP-PARAFAC Method for Interval-wise Missing Network Volume Imputation

Traffic missing data imputation is a fundamental demand and crucial application for real-world intelligent transportation systems. The wide imputation methods in different missing patterns have demonstrated the superiority of tensor learning by effectively characterizing complex spatiotemporal correlations. However, interval-wise missing volume scenarios remain a challenging topic, in particular for long-term continuous missing and high-dimensional data with complex missing mechanisms and patterns. In this paper, we propose a customized tensor decomposition framework, named the data fusion CANDECOMP/PARAFAC (DFCP) tensor decomposition, to combine vehicle license plate recognition (LPR) data and cellphone location (CL) data for the interval-wise missing volume imputation on urban networks. Benefiting from the unique advantages of CL data in the wide spatiotemporal coverage and correlates highly with real-world traffic states, it is fused into vehicle license plate recognition (LPR) data imputation. They are regarded as data types dimension, combined with other dimensions (different segments, time, days), we innovatively design a 4-way low-n-rank tensor decomposition for data reconstruction. Furthermore, to deal with the diverse disturbances in different data dimensions, we derive a regularization penalty coefficient in data imputation. Different from existing regularization schemes, we further introduce Bayesian optimization (BO) to enhance the performance in the non-convexity of the objective function in our regularized hyperparametric solutions during tensor decomposition. Numerical experiments highlight that our proposed method, combining CL and LPR data, significantly outperforms the imputation method using LPR data only. And a sensitivity analysis with varying missing length and rate scenarios demonstrates the robustness of model performance