Strong Collapse for Persistence
We introduce a fast and memory efficient approach to compute the persistent homology (PH) of a sequence of simplicial complexes. The basic idea is to simplify the complexes of the input sequence by using strong collapses, as introduced by J. Barmak and E. Miniam [DCG (2012)], and to compute the PH of an induced sequence of reduced simplicial complexes that has the same PH as the initial one. Our approach has several salient features that distinguishes it from previous work. It is not limited to filtrations (i.e. sequences of nested simplicial subcomplexes) but works for other types of sequences like towers and zigzags. To strong collapse a simplicial complex, we only need to store the maximal simplices of the complex, not the full set of all its simplices, which saves a lot of space and time. Moreover, the complexes in the sequence can be strong collapsed independently and in parallel. As a result and as demonstrated by numerous experiments on publicly available data sets, our approach is extremely fast and memory efficient in practice.
Computational Topology
Topological Data Analysis
Strong Collapse
Persistent homology
Mathematics of computing~Algebraic topology
67:1-67:13
Regular Paper
This research has received funding from the European Research Council (ERC) under the European Union’s Seventh Framework Programme (FP/2007-2013) / ERC Grant Agreement No. 339025 GUDHI (Algorithmic Foundations of Geometry Understanding in Higher Dimensions).
Jean-Daniel
Boissonnat
Jean-Daniel Boissonnat
Université Côte d'Azur, INRIA, France
Siddharth
Pritam
Siddharth Pritam
Université Côte d'Azur, INRIA, France
Divyansh
Pareek
Divyansh Pareek
Indian Institute of Technology Bombay, India
10.4230/LIPIcs.ESA.2018.67
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Jean-Daniel Boissonnat, Siddharth Pritam, and Divyansh Pareek
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