Real-Time Forecasting of Metro Origin-Destination Matrices with High-Order Weighted Dynamic Mode Decomposition
Bibliographic record
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.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".