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

Sophia Loizidou, Andreas Anastasiou, Christophe Ley

TL;DR

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.

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.

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

TL;DR

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.

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.
Paper Structure (18 sections, 27 equations, 7 figures, 7 tables, 2 algorithms)

This paper contains 18 sections, 27 equations, 7 figures, 7 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Derivation of the contrast function
  3. Methodology
  4. Practicalities
  5. Considerations for long signals
  6. Parameter selection
  7. Simulations
  8. Framework
  9. Independent noise structure
  10. von Mises
  11. Different noise structures
  12. Serially correlated data
  13. Real data
  14. Flare data
  15. Acrophase data
  16. ...and 3 more sections

Figures (7)

  • Figure 1: (a) Noiseless signal, $f_t$, of length $T=300$ with change-points at locations $100, 150, 200$. (b) Heatmap of the value of the contrast function evaluated on $f_t$ for $b=150$ and all possible combinations of $s=1,\ldots,150$, $e=151,\ldots,300$.
  • Figure 2: Sequence of length $T=105$ with two change-points at $r_1 = 23$ and $r_2 = 81$. The intervals are checked in the order they appear, from the bottom to the top. Blue intervals indicate that detection of a change-point has occurred.
  • Figure 3: Plots of data sequences that follow model \ref{['eq: model']} with $\epsilon_t \sim \text{vM}(0, \kappa)$ for $\kappa = 1$ with underlying signals (a) \ref{['signal: simple']} and (b) \ref{['signal: simple2']}.
  • Figure 4: Plots of data sequences that follow model \ref{['eq: model']} with $\epsilon_t \sim \text{vM}(0, \kappa)$ for (a) $\kappa = 2$ and (b) $\kappa = 1$ with underlying signals (a) \ref{['signal: complex1']} and (b) \ref{['signal: long']}.
  • Figure 5: Plot of the flare data with the estimated signal from PCID in red.
  • ...and 2 more figures