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 32 articles , 1 standard article )

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  1. Goldfarb, Boris: Singular persistent homology with geometrically parallelizable computation (2020)
  2. Hammarsten, Carl; Helmreich, Rae; Krishnan, Anchala; Meier, John; Schmitz, Nathan: Persistent homology and random models of the Gaussian primes (2020)
  3. Rharbaoui, Wassim; Alayrangues, Sylvie; Lienhardt, Pascal; Peltier, Samuel: Local computation of homology variations over a construction process (2020)
  4. Scaramuccia, Sara; Iuricich, Federico; De Floriani, Leila; Landi, Claudia: Computing multiparameter persistent homology through a discrete Morse-based approach (2020)
  5. Som, Anirudh; Ramamurthy, Karthikeyan Natesan; Turaga, Pavan: Geometric metrics for topological representations (2020)
  6. Daniel Luetgehetmann, Dejan Govc, Jason Smith, Ran Levi: Computing persistent homology of directed flag complexes (2019) arXiv
  7. Dey, Tamal K.; Shi, Dayu; Wang, Yusu: SimBa: an efficient tool for approximating Rips-filtration persistence via Simplicial Batch collapse (2019)
  8. Kerber, Michael; Schreiber, Hannah: Barcodes of towers and a streaming algorithm for persistent homology (2019)
  9. Mémoli, Facundo; Singhal, Kritika: A primer on persistent homology of finite metric spaces (2019)
  10. Michael Lesnick, Matthew Wright: Computing Minimal Presentations and Betti Numbers of 2-Parameter Persistent Homology (2019) arXiv
  11. Salnikov, Vsevolod; Cassese, Daniele; Lambiotte, Renaud: Simplicial complexes and complex systems (2019)
  12. Alan Hylton, Gregory Henselman-Petrusek, Janche Sang, Robert Short: Tuning the Performance of a Computational Persistent Homology Package (2018) arXiv
  13. Dłotko, Paweł; Wanner, Thomas: Rigorous cubical approximation and persistent homology of continuous functions (2018)
  14. Franek, Peter; Krčál, Marek; Wagner, Hubert: Solving equations and optimization problems with uncertainty (2018)
  15. Kusano, Genki; Fukumizu, Kenji; Hiraoka, Yasuaki: Kernel method for persistence diagrams via kernel embedding and weight factor (2018)
  16. Obayashi, Ippei: Volume-optimal cycle: tightest representative cycle of a generator in persistent homology (2018)
  17. Obayashi, Ippei; Hiraoka, Yasuaki; Kimura, Masao: Persistence diagrams with linear machine learning models (2018)
  18. Bauer, Ulrich; Kerber, Michael; Reininghaus, Jan; Wagner, Hubert: \textscPhat-- persistent homology algorithms toolbox (2017)
  19. Bubenik, Peter; Dłotko, Paweł: A persistence landscapes toolbox for topological statistics (2017)
  20. Kerber, Michael; Schreiber, Hannah: Barcodes of towers and a streaming algorithm for persistent homology (2017)

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