On the potential of Optimal Transport in Geospatial Data Science

2024-10-15

arXiv.org

AI Summary

Conventional spatial prediction error metrics (e.g., MAE, MSE) neglect spatial heterogeneity, autocorrelation, and the modifiable areal unit problem (MAUP), leading to error distributions that poorly reflect real-world operational costs—such as vehicle repositioning in mobility systems. Method: This paper introduces Partial Optimal Transport (POT) into geospatial prediction evaluation and modeling for the first time. We propose spatially aware, OT-based evaluation metrics and loss functions that explicitly couple prediction errors with relocation costs (e.g., bike rebalancing). Our approach jointly models spatial distribution structure and solves POT optimization, implemented efficiently using Python and the POT library. Contribution/Results: Evaluated on shared-bike demand forecasting and EV charging station occupancy prediction, our method significantly improves spatial distribution fidelity over standard metrics. It achieves superior alignment between predicted and ground-truth spatial patterns, directly translating to more actionable, cost-aware predictions. The implementation is publicly available.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Machine Learning: Calibration & Uncertainty Quantification
• Search and Optimization: Evaluation and Analysis

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Systems and Infrastructure for Web, Mobile and WoT: Location- and context-aware Web and WoT applications and services
• User Modeling, Personalization and Recommendation: Metrics for user behavior and evaluating success

Abstract

Prediction problems in geographic information science and transportation are often motivated by the possibility to enhance operational efficiency and thereby reduce emissions. Examples range from predicting car sharing demand for relocation planning to forecasting traffic congestion for navigation purposes. However, conventional accuracy metrics ignore the spatial distribution of the errors, despite its relevance for operations. Here, we put forward a spatially aware evaluation metric and loss function based on Optimal Transport (OT). Our framework leverages partial OT and can minimize relocation costs in any spatial prediction problem. We showcase the advantages of OT-based evaluation over conventional metrics and further demonstrate the application of an OT loss function for improving forecasts of bike sharing demand and charging station occupancy. Thus, our framework not only aligns with operational considerations, but also signifies a step forward in refining predictions within geospatial applications. All code is available at https://github.com/mie-lab/geospatialOT.

Problem

• Evaluates spatial error impacts on model utility
• Proposes Optimal Transport for spatial error assessment
• Improves prediction accuracy with spatial cost reduction

Innovation

• Uses Optimal Transport for spatial evaluation
• Quantifies transport costs of prediction errors
• Integrates OT as neural network loss function