Detecting change regions on spheres

2026-03-23

AI Summary

This work addresses the challenge of detecting change regions with complex shapes and irregular boundaries on spherical and other manifolds, where conventional time series methods are inapplicable. The authors propose the CRISP estimator—the first method to extend change-region detection to d-dimensional spherical manifolds—by formulating a signal-plus-noise model and integrating VC dimension theory with spherical geometric analysis. This approach yields a unified framework capable of handling both single and multiple irregular regions, accompanied by theoretical guarantees that explicitly link convergence rates to the VC dimension of the hypothesis class. The proposed multi-region separation algorithm demonstrates strong finite-sample performance and is successfully applied to real-world spherical datasets, including global temperature and ozone hole observations, confirming its effectiveness and practical utility.

Technology Category

• Machine Learning: Learning with Manifolds
• Computer Vision: Other Foundations of Computer Vision
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

Abstract

While change point detection in time series data has been extensively studied, little attention has been given to its generalisation to data observed on spheres or other manifolds, where changes may occur within spatially complex regions with irregular boundaries, posing significant challenges. We propose a new class of estimators, namely, Change Region Identification and SeParation (CRISP), to locate changes in the mean function of a signal-plus-noise model defined on $d$-dimensional spheres. The CRISP estimator applies to scenarios with a single change region, and is extended to multiple change regions via a newly developed generic scheme. The convergence rate of the CRISP estimator is shown to depend on the VC dimension of the hypothesis class that characterises the change regions in general. We also carefully study the case where change regions have the geometry of spherical caps. Simulations confirm the promising finite-sample performance of this approach. The CRISP estimator's practical applicability is further demonstrated through two real data sets on global temperature and ozone hole.

Problem

• change point detection
• spherical data
• manifold
• spatial change regions
• irregular boundaries

Innovation

• change region detection
• spherical data
• CRISP estimator
• manifold learning
• VC dimension