Real-Time Forecasting of Metro Origin-Destination Matrices with High-Order Weighted Dynamic Mode Decomposition

Zhanhong Cheng (), Martin Trépanier () and Lijun Sun ()
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Zhanhong Cheng: Department of Civil Engineering, McGill University, Montreal, Quebec H3A 0C3, Canada; Interuniversity Research Centre on Enterprise Networks, Logistics and Transportation (CIRRELT), Montreal, Quebec H2S 3H1, Canada
Martin Trépanier: Interuniversity Research Centre on Enterprise Networks, Logistics and Transportation (CIRRELT), Montreal, Quebec H2S 3H1, Canada; Department of Mathematics and Industrial Engineering, Polytechnique Montreal, Montreal, Quebec H3T 1J4, Canada
Lijun Sun: Department of Civil Engineering, McGill University, Montreal, Quebec H3A 0C3, Canada; Interuniversity Research Centre on Enterprise Networks, Logistics and Transportation (CIRRELT), Montreal, Quebec H2S 3H1, Canada

Transportation Science, 2022, vol. 56, issue 4, 904-918

Abstract: Forecasting short-term ridership of different origin-destination pairs (i.e., OD matrix) is crucial to the real-time operation of a metro system. However, this problem is notoriously difficult due to the large-scale, high-dimensional, noisy, and highly skewed nature of OD matrices. In this paper, we address the short-term OD matrix forecasting problem by estimating a low-rank high-order vector autoregression (VAR) model. We reconstruct this problem as a data-driven reduced-order regression model and estimate it using dynamic mode decomposition (DMD). The VAR coefficients estimated by DMD are the best-fit (in terms of Frobenius norm) linear operator for the rank-reduced full-size data. To address the practical issue that metro OD matrices cannot be observed in real time, we use the boarding demand to replace the unavailable OD matrices. Moreover, we consider the time-evolving feature of metro systems and improve the forecast by exponentially reducing the weights for historical data. A tailored online update algorithm is then developed for the high-order weighted DMD model (HW-DMD) to update the model coefficients at a daily level, without storing historical data or retraining. Experiments on data from two large-scale metro systems show that the proposed HW-DMD is robust to noisy and sparse data, and significantly outperforms baseline models in forecasting both OD matrices and boarding flow. The online update algorithm also shows consistent accuracy over a long time, allowing us to maintain an HW-DMD model at much low costs.

Keywords: origin-destination matrices; ridership forecasting; dynamic mode decomposition; public transport systems; high-dimensional time series; time-evolving system (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ortrsc:v:56:y:2022:i:4:p:904-918

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