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H 1 The compressed annotation matrix: an efficient data structure for persistent cohomology

Auteurs : Maria, Clément (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : The persistent homology with coefficients in a field F coincides with the same for cohomology because of duality. We propose an implementation of a recently introduced algorithm for persistent cohomology that attaches annotation vectors with the simplices. We separate the representation of the simplicial complex from the representation of the cohomology groups, and introduce a new data structure for maintaining the annotation matrix, which is more compact and reduces substancially the amount of matrix operations. In addition, we propose heuristics to simplify further the representation of the cohomology groups and improve both time and space complexities. The paper provides a theoretical analysis, as well as a detailed experimental study of our implementation and comparison with state-of-the-art software for persistent homology and cohomology.
    persistent cohomology - implementation - matrix reduction - data structure - annotation - simplex tree

    Codes MSC :
    68Wxx - Algorithms

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 28/05/14
      Date de captation : 16/12/13
      Collection : Research talks ; Computer Science
      Format : quicktime ; audio/x-aac
      Durée : 00:34:58
      Domaine : Computer Science
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2013-12-16_Maria.mp4

    Informations sur la rencontre

    Nom de la rencontre : Computational geometry days / Journées de géométrie algorithmique
    Organisateurs de la rencontre : Cohen-Steiner, David ; Mérigot, Quentin
    Dates : 16/12/13 - 20/12/13
    Année de la rencontre : 2013

    Citation Data

    DOI : 10.24350/CIRM.V.18581203
    Cite this video as: Maria, Clément (2013). The compressed annotation matrix: an efficient data structure for persistent cohomology. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18581203
    URI : http://dx.doi.org/10.24350/CIRM.V.18581203


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