Efficient Computation of Persistent Homology for Cubical Data (bibtex)
by Hubert Wagner, Chao Chen, Erald Vucini Abstract
Abstract:
In this paper we present an efficient framework for computation of persistent homology of cubical data in arbitrary dimensions. An existing algorithm using simplicial complexes is adapted to the setting of cubical complexes. The proposed approach enables efficient application of persistent homology in domains where the data is naturally given in a cubical form. By avoiding triangulation of the data, we significantly reduce the size of the complex. We also present a data-structure designed to compactly store and quickly manipulate cubical complexes. By means of numerical experiments, we show high speed and memory efficiency of our approach. We compare our framework to other available implementations, showing its superiority. Finally, we report persistent homology results for selected 3D and 4D data sets.
Reference:
Efficient Computation of Persistent Homology for Cubical Data (Hubert Wagner, Chao Chen, Erald Vucini Abstract), Technical report, PRIP, TU Wien, 2010.
Bibtex Entry:
@TechReport{TR122,
  author =	 "Hubert Wagner and Chao Chen and Erald Vucini
Abstract",
  title =	 "Efficient Computation of Persistent Homology for Cubical Data",
  institution =	 "PRIP, TU Wien",
  number =	 "PRIP-TR-122",
  year =	 "2010",
  url =		 "ftp://ftp.prip.tuwien.ac.at/pub/publications/trs/tr122.pdf",
  abstract =	 "In this paper we present an efficient framework for computation of persistent
homology of cubical data in arbitrary dimensions. An existing
algorithm using simplicial complexes is adapted to the setting of cubical
complexes. The proposed approach enables efficient application of
persistent homology in domains where the data is naturally given in a
cubical form. By avoiding triangulation of the data, we significantly reduce
the size of the complex. We also present a data-structure designed
to compactly store and quickly manipulate cubical complexes. By means
of numerical experiments, we show high speed and memory efficiency of
our approach. We compare our framework to other available implementations,
showing its superiority. Finally, we report persistent homology
results for selected 3D and 4D data sets.",
}
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