Cascade of phase transitions for multiscale clustering

Tony Bonnaire, Aurélien Decelle, and Nabila Aghanim
Phys. Rev. E 103, 012105 – Published 6 January 2021

Abstract

We present a framework exploiting the cascade of phase transitions occurring during a simulated annealing of the expectation-maximization algorithm to cluster datasets with multiscale structures. Using the weighted local covariance, we can extract, a posteriori and without any prior knowledge, information on the number of clusters at different scales together with their size. We also study the linear stability of the iterative scheme to derive the threshold at which the first transition occurs and show how to approximate the next ones. Finally, we combine simulated annealing together with recent developments of regularized Gaussian mixture models to learn a principal graph from spatially structured datasets that can also exhibit many scales.

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  • Received 13 August 2020
  • Revised 15 October 2020
  • Accepted 2 December 2020

DOI:https://doi.org/10.1103/PhysRevE.103.012105

©2021 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

Tony Bonnaire1,2, Aurélien Decelle2,3, and Nabila Aghanim1

  • 1Université Paris-Saclay, CNRS, Institut d'Astrophysique Spatiale, 91405 Orsay, France
  • 2Université Paris-Saclay, TAU Team INRIA Saclay, CNRS, Laboratoire de Recherche en Informatique, 91190 Gif-sur-Yvette, France
  • 3Departamento de Física Téorica I, Universidad Complutense, 28040 Madrid, Spain

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Vol. 103, Iss. 1 — January 2021

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