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Laplacian Convolutional Representation for Traffic Time Series Imputation (2212.01529v3)

Published 3 Dec 2022 in cs.LG and cs.AI

Abstract: Spatiotemporal traffic data imputation is of great significance in intelligent transportation systems and data-driven decision-making processes. To perform efficient learning and accurate reconstruction from partially observed traffic data, we assert the importance of characterizing both global and local trends in time series. In the literature, substantial works have demonstrated the effectiveness of utilizing the low-rank 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 as a circular convolution. Then, we develop a low-rank Laplacian convolutional representation (LCR) model by putting the circulant matrix nuclear norm and the Laplacian kernelized temporal regularization together, which is proved to meet a unified framework that has a fast Fourier transform (FFT) solution in log-linear time complexity. Through extensive experiments on several traffic datasets, we demonstrate the superiority of LCR over several baseline models for imputing traffic time series of various time series behaviors (e.g., data noises and strong/weak periodicity) and reconstructing sparse speed fields of vehicular traffic flow. The proposed LCR model is also an efficient solution to large-scale traffic data imputation over the existing imputation models.

Citations (12)

Summary

  • The paper introduces the Laplacian Conv. Representation model that integrates global low-rank structures with local temporal trends for precise traffic data imputation.
  • It leverages an FFT-based algorithm achieving log-linear complexity, outperforming traditional low-rank methods in scalability and efficiency.
  • Extensive experiments on real-world traffic datasets demonstrate the model's superior accuracy even under high missing data conditions.

Laplacian Convolutional Representation for Traffic Time Series Imputation

The paper tackles the challenge of traffic time series imputation within intelligent transportation systems (ITS), focusing on the need to efficiently learn and accurately reconstruct data that may be incomplete or noisy. It introduces a novel model called Laplacian Convolutional Representation (LCR), which leverages both the global and local trends inherent in traffic data.

Overview

Traffic data imputation is crucial for various ITS applications such as route planning and traffic forecasting. ITS data often suffer from issues like sensor malfunctions or network disruptions, leading to missing data. Traditional methods, such as low-rank matrix/tensor completion models, have demonstrated efficacy by exploiting the low-rank nature of traffic data. However, these approaches often fail to adequately capture both global and local dynamics.

The LCR model integrates a Laplacian kernel to provide temporal regularization, effectively capturing local trends through circular convolution. This novel approach combines the circulant matrix nuclear norm for global trend modeling with the Laplacian kernel, leading to a unified framework that can be solved efficiently using the Fast Fourier Transform (FFT). The process is characterized by a log-linear time complexity, which offers significant improvements in scalability over existing models.

Numerical Results

The paper presents extensive experiments using several traffic datasets, demonstrating the superiority of LCR over existing baseline models. Key results highlight LCR's capability to handle various traffic time series behaviors, including noise and strong or weak periodicity. For instance, traffic speed and volume data from real-world scenarios were reconstructed with high accuracy, even when significant portions of the data were missing.

In terms of performance metrics, the proposed LCR model consistently outperformed other models across different missing data rates. The structured experiments underscore the importance of combining global low-rank structures with local temporal modeling to achieve enhanced reconstruction accuracy. The LCR's use of a fast FFT-based algorithm also addresses the computational inefficiencies faced by more traditional methods.

Implications and Future Directions

The implications of this research are both practical and theoretical. Practically, the LCR model provides a robust solution for large-scale traffic data imputation, vital for real-time applications in ITS. It improves the accuracy of data-driven decision-making processes that rely on complete and accurate data.

Theoretically, the introduction of the Laplacian kernelized regularization within the low-rank framework marks a significant advancement. By bridging the gaps between traditional low-rank models and graph-Laplacian methods, it opens up new possibilities for modeling in various domains beyond transportation.

In terms of future research, the paper suggests exploring broader applications of this model. The principles of LCR, namely the integration of circulant matrix properties and temporal regularization, could be adapted for time series prediction and forecasting tasks across different fields. Further investigation into optimizing the kernel design and adapting the framework to other types of spatiotemporal data is also a promising direction.

In conclusion, the LCR model presents a substantial advancement in traffic data imputation, providing both theoretical insights and practical tools for handling incomplete and noisy datasets in an efficient manner.

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