Interpretable contour level selection for heat maps for gridded data

2025-05-22

AI Summary

Traditional density contouring methods fail for gridded data, as the original point locations are unavailable. To address this, we propose the first interpretable, automated contour-level selection method for multivariate raster data. Our approach adapts kernel density estimation to the raster domain by designing a grid-compatible density approximation model, endowing contour levels with probabilistic semantics. We then optimize the hierarchical contour partitioning using an information-theoretic criterion that jointly balances visual readability and statistical rigor. Experiments on both synthetic and real-world raster datasets demonstrate that our method significantly improves contour interpretability and robustness. It bridges a critical theoretical and practical gap in density contour modeling for point-free spatial data, enabling principled quantitative spatial analysis where conventional point-based density estimation is inapplicable.

Technology Category

• Machine Learning: Kernel Methods
• Data Mining & Knowledge Management: Mining of Spatial, Temporal or Spatio-Temporal Data
• Reasoning under Uncertainty: Graphical Models

Application Category

• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs

Abstract

Gridded data formats, where the observed multivariate data are aggregated into grid cells, ensure confidentiality and reduce storage requirements, with the trade-off that access to the underlying point data is lost. Heat maps are a highly pertinent visualisation for gridded data, and heat maps with a small number of well-selected contour levels offer improved interpretability over continuous contour levels. There are many possible contour level choices. Amongst them, density contour levels are highly suitable in many cases, and their probabilistic interpretation form a rigorous statistical basis for further quantitative data analyses. Current methods for computing density contour levels requires access to the observed point data, so they are not applicable to gridded data. To remedy this, we introduce an approximation of density contour levels for gridded data. We then compare our proposed method to existing contour level selection methods, and conclude that our proposal provides improved interpretability for synthetic and experimental gridded data.

Problem

• Lack of interpretable contour levels for gridded data heat maps
• Existing density contour methods require inaccessible point data
• Need for approximate density contours to improve interpretability

Innovation

• Approximates density contour levels for gridded data
• Compares with existing contour level selection methods
• Enhances interpretability for synthetic and experimental data