Robust measures of dispersion for circular data with an anomaly detection rule

2026-03-01

AI Summary

This study addresses the lack of robustness in estimating dispersion for circular data under outlier contamination. For the first time, it extends three linear robust dispersion measures to the circular domain, analyzing their robustness through influence functions and relative deviation curves. The authors develop high-breakdown-point, high-efficiency parameter estimators tailored for von Mises and wrapped normal distributions. Furthermore, they propose a novel circular anomaly detection method and introduce circular violin plots for intuitive outlier visualization. Extensive Monte Carlo simulations and experiments on three real-world datasets demonstrate that the proposed approach significantly outperforms existing methods in both estimation accuracy and outlier detection capability.

Technology Category

• Data Mining & Knowledge Management: Anomaly/Outlier Detection
• Intelligent Robots: State Estimation
• Computer Vision: Adversarial Attacks & Robustness

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Responsible Web: Measurement, analysis, and circumvention of Web censorship
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs

Abstract

Circular variables that represent directions or periodic observations arise in many fields, such as biology and environmental sciences. An important issue when dealing with circular data is how to estimate their dispersion robustly, avoiding undue effects of anomalies. This work extends three robust dispersion measures from the line to the circle. Their robustness is studied via their influence functions and relative bias curves. From these dispersion measures, robust estimators of parameters of circular distributions can be derived. This yields robust estimators for the concentration parameter of the von Mises distribution and the dispersion parameter of the wrapped normal distribution. Their breakdown values and statistical efficiencies are obtained, and they are compared in a simulation study. Building on the best performing estimator, a robust circular anomaly detection procedure is developed, and employed to visualize outliers through a circular violin plot. Three real datasets are analyzed.

Problem

• circular data
• robust dispersion
• anomaly detection
• outliers
• influence function

Innovation

• robust dispersion
• circular data
• anomaly detection
• influence function
• circular violin plot