Robust Matrix Completion for Spatiotemporal Traffic Data in Time–Frequency Domain

Traffic data analysis often faces challenges such as missing data and anomalies, significantly limiting accurate understanding and forecasting of traffic patterns. To address these challenges, our study introduces the anti-circulant-structured tensor Robust Matrix Completion (circ-RMC), a novel approach to enhance spatiotemporal traffic flow data analysis. Traditional Robust Matrix Completion (RMC) methods struggle with continuous missing data and often overlook local traffic dynamics due to the assumption on global data. Our proposed circ-RMC overcomes these limitations by integrating the Short-Time Fourier Transform (STFT) with RMC, enabling more accurate data completion and anomaly detection in the time-frequency domain. This method uniquely analyzes traffic flow as a multivariate time series matrix, using STFT to detect localized changes in traffic patterns over time. The resulting time-frequency spectra are then organized into an anti-circulant-structured tensor, capturing intricate correlations across different locations. In addition, the model is adept at detecting continuous anomalous behavior caused by special events. Formulated as an optimization problem, this method employs the Alternating Direction Method of Multipliers (ADMM) for efficient resolution. Tested against real-world taxi passenger flow and bike-sharing records, circ-RMC outperforms existing methodologies in completing missing data and identifying traffic anomalies. This approach contributes to traffic management and urban planning by providing complete datasets for downstream traffic-related tasks and offering researchers a tool to understand and explore travel behaviors.