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 12 articles , 1 standard article )

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  1. Bauer, Ulrich; Kerber, Michael; Reininghaus, Jan; Wagner, Hubert: Phat -- persistent homology algorithms toolbox (2017)
  2. Bubenik, Peter; Dłotko, Paweł: A persistence landscapes toolbox for topological statistics (2017)
  3. Toth, Csaba D. (ed.); Goodman, Jacob E. (ed.); O’Rourke, Joseph (ed.): Handbook of discrete and computational geometry (2017)
  4. Dey, Tamal K.; Shi, Dayu; Wang, Yusu: Simba: an efficient tool for approximating rips-filtration persistence via simplicial batch-collapse (2016)
  5. Zeppelzauer, Matthias; Zieliński, Bartosz; Juda, Mateusz; Seidl, Markus: Topological descriptors for 3D surface analysis (2016)
  6. Boissonnat, Jean-Daniel; Dey, Tamal K.; Maria, Clément: The compressed annotation matrix: an efficient data structure for computing persistent cohomology (2015)
  7. Halperin, Dan; Kerber, Michael; Shaharabani, Doron: The offset filtration of convex objects (2015)
  8. Bauer, Ulrich; Kerber, Michael; Reininghaus, Jan: Clear and compress: computing persistent homology in chunks (2014)
  9. Bauer, Ulrich; Kerber, Michael; Reininghaus, Jan; Wagner, Hubert: PHAT -- persistent homology algorithms toolbox (2014)
  10. Brittany Terese Fasy, Jisu Kim, Fabrizio Lecci, Clement Maria: Introduction to the R package TDA (2014) arXiv
  11. Hong, Hoon (ed.); Yap, Chee (ed.): Mathematical software -- ICMS 2014. 4th international congress, Seoul, South Korea, August 5--9, 2014. Proceedings (2014)
  12. Kasten, Jens; Reininghaus, Jan; Reich, Wieland; Scheuermann, Gerik: Toward the extraction of saddle periodic orbits (2014)