On the consistent and scalable detection of spatial patterns.

2026-02-02

arXiv.org

AI Summary

Existing methods for spatial pattern detection lack statistical consistency and struggle to scale to large-scale spatial omics data. This work unifies prevailing approaches within a quadratic form statistical framework, establishing—for the first time—a theoretical foundation for consistent spatial pattern detection. We derive general conditions under which such methods achieve consistency and propose a scalable, corrected algorithm that efficiently and robustly handles datasets with millions of spatial locations. The method’s effectiveness is validated on real single-cell lineage tracing data, demonstrating substantial improvements in both reliability and scalability for large-scale spatial omics analysis.

Technology Category

• Data Mining & Knowledge Management: Mining of Spatial, Temporal or Spatio-Temporal Data
• Machine Learning: Other Foundations of Machine Learning
• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Security and Privacy: Large-scale security measurements

Abstract

Detecting spatial patterns is fundamental to scientific discovery, yet current methods lack statistical consensus and face computational barriers when applied to large-scale spatial omics datasets. We unify major approaches through a single quadratic form and derive general consistency conditions. We reveal that several widely used methods, including Moran's I, are inconsistent, and propose scalable corrections. The resulting test enables robust pattern detection across millions of spatial locations and single-cell lineage-tracing datasets.

Problem

• spatial patterns
• statistical consistency
• scalability
• spatial omics
• computational barriers

Innovation

• spatial pattern detection
• statistical consistency
• quadratic form
• scalable correction
• spatial omics