PHAT - Persistent Homology Algorithms Toolbox. PHAT is a C++ library for the computation of persistent homology. This task is usually split into two major tasks: (1) building a boundary matrix representation of the given filtration and (2) bringing it into a reduced form by elementary matrix operations. PHAT focuses entirely on the latter step. We aim for a simple generic design that allows for flexibility, without sacrificing efficiency or user-friendliness. This makes PHAT a versatile platform for experimenting with novel algorithmic ideas and comparing them to state of the art implementations. A major aspect of PHAT is to decouple the reduction strategy from the representation of the boundary matrix and the low-level operations to query and manipulate it. We recap the reduction algorithms currently implemented in PHAT as well as the available representation types. In particular, we decribe a novel approach that transforms a column of the matrix into an intermediate data structure that is more suitable for efficient manipulations. We show in experimental evaluations that the choice of a suitable representation has an equally important effect on the practical performance as the choice of the reduction strategy.

References in zbMATH (referenced in 41 articles , 1 standard article )

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  1. Grbić, Jelena; Wu, Jie; Xia, Kelin; Wei, Guo-Wei: Aspects of topological approaches for data science (2022)
  2. Lesnick, Michael; Wright, Matthew: Computing minimal presentations and bigraded Betti numbers of 2-parameter persistent homology (2022)
  3. Alpert, Hannah; Kahle, Matthew; MacPherson, Robert: Configuration spaces of disks in an infinite strip (2021)
  4. Bauer, Ulrich: Ripser: efficient computation of Vietoris-Rips persistence barcodes (2021)
  5. Calcina, Sabrina S.; Gameiro, Marcio: Parameter estimation in systems exhibiting spatially complex solutions via persistent homology and machine learning (2021)
  6. Feng, Michelle; Porter, Mason A.: Persistent homology of geospatial data: a case study with voting (2021)
  7. Cang, Zixuan; Wei, Guo-Wei: Persistent cohomology for data with multicomponent heterogeneous information (2020)
  8. Goldfarb, Boris: Singular persistent homology with geometrically parallelizable computation (2020)
  9. Hammarsten, Carl; Helmreich, Rae; Krishnan, Anchala; Meier, John; Schmitz, Nathan: Persistent homology and random models of the Gaussian primes (2020)
  10. Rharbaoui, Wassim; Alayrangues, Sylvie; Lienhardt, Pascal; Peltier, Samuel: Local computation of homology variations over a construction process (2020)
  11. Scaramuccia, Sara; Iuricich, Federico; De Floriani, Leila; Landi, Claudia: Computing multiparameter persistent homology through a discrete Morse-based approach (2020)
  12. Som, Anirudh; Ramamurthy, Karthikeyan Natesan; Turaga, Pavan: Geometric metrics for topological representations (2020)
  13. Daniel Luetgehetmann, Dejan Govc, Jason Smith, Ran Levi: Computing persistent homology of directed flag complexes (2019) arXiv
  14. Dey, Tamal K.; Shi, Dayu; Wang, Yusu: SimBa: an efficient tool for approximating Rips-filtration persistence via Simplicial Batch collapse (2019)
  15. Kerber, Michael; Schreiber, Hannah: Barcodes of towers and a streaming algorithm for persistent homology (2019)
  16. Mémoli, Facundo; Singhal, Kritika: A primer on persistent homology of finite metric spaces (2019)
  17. Michael Lesnick, Matthew Wright: Computing Minimal Presentations and Betti Numbers of 2-Parameter Persistent Homology (2019) arXiv
  18. Salnikov, Vsevolod; Cassese, Daniele; Lambiotte, Renaud: Simplicial complexes and complex systems (2019)
  19. Alan Hylton, Gregory Henselman-Petrusek, Janche Sang, Robert Short: Tuning the Performance of a Computational Persistent Homology Package (2018) arXiv
  20. Boissonnat, Jean-Daniel; Pritam, Siddharth; Pareek, Divyansh: Strong collapse for persistence (2018)

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