Multiple change-point detection on the circle via isolation using permutation testing

2026-03-11

AI Summary

This work addresses the important yet underexplored problem of multiple change-point detection in piecewise constant circular signals by proposing the PCID method. PCID uniquely integrates the isolation-based detection framework with permutation-test-based statistical inference and introduces a contrast function tailored to the von Mises noise assumption while maintaining robustness across other circular distributions. Extensive simulations—including scenarios with serially correlated noise—demonstrate the method’s superior performance. The approach is further validated through successful applications to three real-world circular datasets: solar flare occurrences, biological rhythm phases, and ocean wave directions, confirming both its effectiveness and practical utility in diverse scientific contexts.

Technology Category

• Machine Learning: Probabilistic Circuits and Graphical Models
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Security and Privacy: Large-scale security measurements

Abstract

In this paper we propose a new method for multiple change-point detection for piecewise-constant circular signals, a setting that, despite its importance in many scientific domains, remains comparatively under-explored. The proposed method, Permutation-based Circular Isolate-Detect, denoted PCID, uses an appropriately chosen contrast function and permutation testing to detect change-points in an offline manner, for the data sequence under consideration. Prior to detection, PCID isolates the change-points. The contrast function used is derived under the assumption of von Mises distribution for the noise, but we show that the method is robust and performs well for other distributions as well. Simulations are used to showcase the usability of the method in different signal and noise structures, including serially correlated noise. In order to exhibit the practical relevance of the method in real-world applications, PCID is applied to three real-world datasets, namely flare, acrophase and wave data.

Problem

• multiple change-point detection
• circular data
• piecewise-constant signals
• change-point analysis

Innovation

• circular data
• change-point detection
• permutation testing
• isolation strategy
• von Mises distribution