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Graph Based Approach for Galaxy Filament Extraction

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Complex Networks & Their Applications XII (COMPLEX NETWORKS 2023)

Part of the book series: Studies in Computational Intelligence ((SCI,volume 1143))

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Abstract

We propose an original density estimator built from a cloud of points \( \mathcal {X}^{}_{ } \subset \mathbb R ^d\). To do this, we consider geometric graphs \(\mathcal {G}(\mathcal {X}^{}_{ }, \ r)\) on the cloud. These graphs depend on a radius r. By varying the radius, we see the emergence of large components around certain critical radii, which is the phenomenon of continuum percolation. Percolation allows us to have both a local view of the data (through local constraints on the radius r) and a global one (the emergence of macro-structures). With this tool, we address the problem of galaxy filament extraction. The density estimator gives us a relevant graph on galaxies. With an algorithm sharing the ideas of the Fréchet mean, we extract a subgraph from this graph, the galaxy filaments.

The first author would like to thank the Université Côte d’Azur (UCA) DS4H Investments in the Future project managed by the National Research Agency (ANR, reference number ANR-17-EURE-0004) and 3IA Côte d’Azur for partial funding of his PhD thesis. All the authors acknowledge a partial support by Nokia Bell Labs “Distributed Learning and Control for Network Analysis” and Bpifrance in collaboration with Airbus D &S (LiChIE contract, 2020–2024).

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Notes

  1. 1.

    Those ‘filaments’ are relatively thick and have a non-negligible width; a real 1D-manifold would not have a density w.r.t. the Lebesgue measure.

  2. 2.

    But still \(p_\infty (r_c) = 0\). Although it is widely accepted that for any \(d \ge 2\), \(p_\infty (r_c) = 0\), this has only been proved for \(d = 2\) (cf. theorem 4.5 by Meester & Roy [23] and by Tanemura for d sufficiently large [30]).

  3. 3.

    Thanks to Vinay Kumar [33] for sharing the data.

  4. 4.

    Thanks to the authors of the article “Detection of cosmic filaments using the Candy model” [29] for the generation of the data used herein. These data were kindly supplied by Radu Stoica, Enn Saar and Vicent Martínez.

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Authors and Affiliations

  1. Inria, Université Côte d’Azur, Sophia-Antipolis, France

    Louis Hauseux, Konstantin Avrachenkov & Josiane Zerubia

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  1. Louis Hauseux
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  2. Konstantin Avrachenkov
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  3. Josiane Zerubia
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Correspondence to Louis Hauseux .

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Editors and Affiliations

  1. University of Burgundy, Dijon Cedex, France

    Hocine Cherifi

  2. Thomas J. Watson College of Engineering and Applied Science, Binghamton University, Binghamton, NY, USA

    Luis M. Rocha

  3. IUT Lumière - Université Lyon 2, University of Lyon, Bron, France

    Chantal Cherifi

  4. Department of Economics, Yildiz Technical University, Istanbul, Türkiye

    Murat Donduran

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Hauseux, L., Avrachenkov, K., Zerubia, J. (2024). Graph Based Approach for Galaxy Filament Extraction. In: Cherifi, H., Rocha, L.M., Cherifi, C., Donduran, M. (eds) Complex Networks & Their Applications XII. COMPLEX NETWORKS 2023. Studies in Computational Intelligence, vol 1143. Springer, Cham. https://doi.org/10.1007/978-3-031-53472-0_32

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  • DOI: https://doi.org/10.1007/978-3-031-53472-0_32

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