Real-time forecasting of metro origin-destination matrices with high-order weighted dynamic mode decomposition

TL;DR

This paper introduces HW-DMD, a novel real-time forecasting model for metro origin-destination matrices that effectively handles high-dimensional, noisy, and sparse data, outperforming existing methods.

Contribution

The paper develops a high-order weighted dynamic mode decomposition model with an online update algorithm for accurate, real-time metro OD matrix forecasting.

Findings

HW-DMD outperforms baseline models in accuracy

The model is robust to noisy and sparse data

Online updates maintain accuracy over time

Abstract

Forecasting the short-term ridership among origin-destination pairs (OD matrix) of a metro system is crucial in real-time metro operation. However, this problem is notoriously difficult due to the high-dimensional, sparse, noisy, and skewed nature of OD matrices. This paper proposes a High-order Weighted Dynamic Mode Decomposition (HW-DMD) model for short-term metro OD matrices forecasting. DMD uses Singular Value Decomposition (SVD) to extract low-rank approximation from OD data, and a low-rank high-order vector autoregression model is established for forecasting. To address a practical issue that metro OD matrices cannot be observed in real-time, we use the boarding demand to replace the unavailable OD matrices. Particularly, we consider the time-evolving feature of metro systems and improve the forecast by exponentially reducing the weights for old data. Moreover, we develop a tailored online update algorithm for HW-DMD to update the model coefficients daily without storing historical data or retraining. Experiments on data from a large-scale metro system show the proposed HW-DMD is robust to the 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 when maintaining an HW-DMD model at low costs.