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arxiv: 2605.00083 · v1 · submitted 2026-04-30 · 💻 cs.LG

Comparative Analysis of Polygon-Based and Global Machine Learning Models for Bus Occupancy Prediction

Daniel Azenkot , Michael Fire , Eran Ben Elia This is my paper

Pith reviewed 2026-05-09 20:26 UTC · model grok-4.3

classification 💻 cs.LG
keywords bus occupancy predictionspatial clusteringmachine learning modelspublic transport forecastinglocal vs global modelspolygon-based analysisridership prediction
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The pith

Clustering bus stops into spatial polygons and training local models for each yields bus occupancy forecasts as accurate as one city-wide global model.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper tests whether splitting a city into polygon regions of nearby bus stops, then training a separate machine learning model on each region, can predict passenger numbers as well as a single model trained on all stops together. The local models use the same mix of features: time of day, day of week, weather, and nearby attractions. If the local versions perform equally well, transit planners could build forecasts tuned to specific neighborhoods without losing overall reliability. The work compares the two strategies on real bus data and finds comparable accuracy between them.

Core claim

By grouping bus stops into polygons on the principle that nearby stops share similar ridership patterns, and training a dedicated forecasting model for each polygon using temporal, meteorological, and spatial features, the localized approach achieves predictive accuracy comparable to that of a single global model applied across the entire urban area.

What carries the argument

Polygon-based spatial clustering of bus stops, which groups proximate stops assumed to have similar ridership characteristics so that a separate machine learning model can be trained per cluster.

If this is right

  • Transit agencies could run neighborhood-specific forecasts while maintaining city-level reliability.
  • Local models allow service adjustments targeted to individual polygons rather than uniform city rules.
  • The same multi-source feature set (time, weather, attractions) supports both local and global training without modification.
  • Spatially aware clustering offers a practical alternative to treating the whole city as one homogeneous area.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same polygon clustering idea could be tested on other transport modes such as trains or shared bikes where stop proximity also matters.
  • Agencies might lower training costs by maintaining many small local models instead of one large global model.
  • Dynamic polygons that shift with seasons or events could be explored as an extension beyond fixed boundaries.

Load-bearing premise

Bus stops that are close together share similar enough ridership characteristics that they can be grouped into polygons and modeled separately without reducing overall forecast accuracy.

What would settle it

If, on the same held-out bus ridership dataset, the polygon-specific models produce measurably lower accuracy than the single global model across standard error metrics, the claim of comparable performance would not hold.

Figures

Figures reproduced from arXiv: 2605.00083 by Daniel Azenkot, Eran Ben Elia, Michael Fire.

Figure 1
Figure 1. Figure 1: Methodology overview. Since PT demand is strongly influenced by stop location, many researchers have developed spatially aware models that incorporate geographic information into their features. These models are based on Tobler’s first law (see [17]), which state that geographically closer or more similar areas tend to exhibit similar patterns. Wang et al. [26] used Geographically Weighted Regression (GWR)… view at source ↗
Figure 2
Figure 2. Figure 2: Max-p regions for March (training on all days except the last 7). Bus stops are grouped into spatially contiguous regions, shown in different colors, as determined by the optimal threshold τ selected using the Calinski–Harabasz (CH) index. effect size analysis. For the high-performing tree-based mod￾els, the effect size remains in the “small” to “negligible” range (e.g., δ = 0.194 for LightGBM and δ = 0.13… view at source ↗
Figure 3
Figure 3. Figure 3: sMPAE of LightGBM across ridership buckets (0–10 to 41–50) over all experiments, comparing global and polygon strategies. Both approaches show similar performance, with the highest errors in the lowest ridership bucket and a monotone increase in error from 11–20 up to 41–50 ridership. Figure S8 shows that extending the LightGBM training set to include the second-to-last week did not yield meaningful improv… view at source ↗
Figure 4
Figure 4. Figure 4: Distribution of mean absolute error (MAE) for four tree-based models (XGBoost, LightGBM, CatBoost, and Random Forest) under the global and polygon-based strategies, for all the test sets used in the experiment. The boxplots show that both approaches yield comparable error distributions, with the polygon-based models generally achieving slightly lower median MAE values. that both modeling strategies maintai… view at source ↗
Figure 5
Figure 5. Figure 5: SHAP values for January (polygon-level LightGBM). sengers. Although the polygon-wise model achieved slightly lower median errors in both weeks, the differences were mi￾nor. The stability of MAE across weeks suggests that the temporal variability of ridership patterns limits the benefit of simple training set extensions, highlighting the need for more adaptive temporal features or dynamic learning mechanism… view at source ↗
read the original abstract

Accurate forecasting of bus ridership (passengers numbers) is crucial for efficient management and optimization of public transport systems. Traditional forecasting models often fail to capture the unique and localized dynamics of different urban areas by treating the entire city as a single, homogeneous region. This paper introduces a novel framework that enhances bus ridership prediction by integrating a spatial clustering methodology with multi-dimensional feature analysis. The proposed framework utilizes a diverse set of data, including bus ridership data (by route number, time, and bus stop) complemented by a variety of open source data, such as spatial features (e.g., attractive destinations), meteorological conditions (e.g., temperature, rainfall), and temporal patterns (e.g., time of day, day of week). By clustering the urban area into distinct regions, based on the principle that bus stops in close proximity share similar ridership characteristics, a separate local forecasting model is trained for each of these clusters. This localized approach demonstrates an accuracy comparable to that of global models. The findings suggest that a spatially-aware, localized modeling strategy is effective for public transport prediction, paving the way for more targeted and efficient service improvements.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript proposes a framework for bus occupancy prediction that integrates spatial clustering of bus stops into polygons (based on proximity) with per-cluster machine learning models trained on multi-feature data including ridership, spatial attributes of destinations, meteorological variables, and temporal patterns. It claims that these localized polygon-based models achieve accuracy comparable to a single global model trained on the full dataset.

Significance. If the empirical comparison holds under proper validation, the work could support more spatially targeted forecasting in public transit, potentially improving operational efficiency. The reliance on open-source auxiliary data is a methodological strength that enhances reproducibility and generalizability.

major comments (2)
  1. Abstract: The central claim that 'this localized approach demonstrates an accuracy comparable to that of global models' is stated without any quantitative metrics (e.g., MAE, RMSE, R²), error bars, baseline details, or statistical tests. This absence makes the primary result unverifiable from the provided text and is load-bearing for the paper's contribution.
  2. Methodology (clustering and evaluation procedure): No description is given of the specific clustering algorithm, how the number of polygons/clusters is determined, the criteria for assigning stops to polygons, the train/validation/test split strategy, or the cross-validation method used to compare local versus global models. These details are required to assess whether the 'comparable accuracy' result is robust or an artifact of the experimental design.
minor comments (1)
  1. The abstract and introduction would benefit from a concise statement of the exact performance metrics and the magnitude of any observed differences between local and global models.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and detailed comments on our manuscript. We address each major point below and will revise the paper to improve the verifiability and reproducibility of our results.

read point-by-point responses

  1. Referee: Abstract: The central claim that 'this localized approach demonstrates an accuracy comparable to that of global models' is stated without any quantitative metrics (e.g., MAE, RMSE, R²), error bars, baseline details, or statistical tests. This absence makes the primary result unverifiable from the provided text and is load-bearing for the paper's contribution.

    Authors: We agree that the abstract should contain quantitative support for the comparability claim to allow immediate verification. The results section of the manuscript reports MAE, RMSE, and R² values for the polygon-based models versus the single global model (using the same feature set), along with the baselines and a note that performance differences fall within statistical noise. We will revise the abstract to include the key aggregate metrics and a brief reference to the statistical comparison, ensuring the central result is verifiable from the abstract. revision: yes

  2. Referee: Methodology (clustering and evaluation procedure): No description is given of the specific clustering algorithm, how the number of polygons/clusters is determined, the criteria for assigning stops to polygons, the train/validation/test split strategy, or the cross-validation method used to compare local versus global models. These details are required to assess whether the 'comparable accuracy' result is robust or an artifact of the experimental design.

    Authors: We acknowledge that the current description of the clustering and evaluation procedure is insufficiently detailed. We will expand the Methodology section to specify the clustering algorithm, the criterion or method used to select the number of polygons, the precise assignment rule for bus stops, the train/validation/test partitioning approach (including how temporal ordering is respected), and the cross-validation procedure employed for the local-versus-global comparison. These additions will enable readers to assess the robustness of the reported accuracy comparability. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper is an empirical comparative study that clusters bus stops into polygons by spatial proximity, extracts features from external open-source spatial/meteorological/temporal data, trains separate supervised models per cluster, and reports that their accuracy is comparable to a single global model. This workflow contains no mathematical derivation chain; the central claim is a direct outcome of standard clustering plus ML training/evaluation on held-out data. No step defines a quantity in terms of itself, renames a fitted parameter as a prediction, or relies on a self-citation whose content is itself unverified or tautological. The methodology is self-contained against external benchmarks and does not reduce to its inputs by construction.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on the domain assumption of spatial similarity in ridership and on standard machine-learning modeling assumptions. No new physical entities are postulated. Several free parameters are implicit in any clustering-plus-modeling pipeline.

free parameters (2)
  • number of clusters / polygon count
    The number of regions is chosen or optimized from data and directly determines the localization granularity.
  • model hyperparameters
    Typical supervised learning parameters (learning rate, tree depth, regularization, etc.) are tuned to the ridership dataset.
axioms (2)
  • domain assumption Bus stops in close proximity share similar ridership characteristics
    Explicitly invoked in the abstract as the principle justifying the spatial clustering step.
  • domain assumption Integration of open-source spatial, meteorological, and temporal features improves predictive accuracy
    Assumed when the framework is described as using these complementary data sources.

pith-pipeline@v0.9.0 · 5502 in / 1553 out tokens · 38022 ms · 2026-05-09T20:26:04.880697+00:00 · methodology

discussion (0)

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