Regensburg 2022 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 44: Poster Session: Statistical Physics and Critical Phenomena

DY 44.14: Poster

Donnerstag, 8. September 2022, 15:00–18:00, P2

Phase transition in clustering algorithms — •Julian Zitterich and Alexander K. Hartmann — Institute of Physics, University of Oldenburg, Germany

A well known problem in data analysis and machine learning is the clustering problem. It consists of grouping a set of data vectors into subsets, such that similar vectors end up in the same subset. How to define similarity and how to find these subgroups depend much on the investigated problem, thus many algorithms and metrics exists. Also it may that an algorithm is not able to successfully detect structure in the given data. Thus, we study here ensembles of artificially generated data controlled by parameters such that for some parameter values the clustering is easy or at least possible while for other values it is hard or impossible. Thus, from a statistical physics viewpoint we are interested in phase transitions of the clustering problem between such phases. Previously, the existence of such phase transitions was observed for a single ensemble in high-dimensional space by using the AMP algorithm [1]. Here, we investigate numerically [2] four different state-of-the-art cluster algorithms and analyse their behaviour for increasingly complex ensembles. Low complexity ensembles are realized by direct sampling of data vectors, while high complexity ensembles are implemented by short simulations of simple models of interacting particles.

[1] T. Lesieur et al., 54th Annual Allerton Conference on Communication, Control, and Computing (Allerton), arXiv:1610.02918 (2016)

[2] A.K. Hartmann, Big Practical Guide to Computer Simulations, World Scientific (2015)