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Topological Methods in Data Analysis and Visualization IIIClear and Compress: Computing Persistent Homology in Chunks

Topological Methods in Data Analysis and Visualization III: Clear and Compress: Computing... [We present a parallel algorithm for computing the persistent homology of a filtered chain complex. Our approach differs from the commonly used reduction algorithm by first computing persistence pairs within local chunks, then simplifying the unpaired columns, and finally applying standard reduction on the simplified matrix. The approach generalizes a technique by Günther et al., which uses discrete Morse Theory to compute persistence; we derive the same worst-case complexity bound in a more general context. The algorithm employs several practical optimization techniques, which are of independent interest. Our sequential implementation of the algorithm is competitive with state-of-the-art methods, and we further improve the performance through parallel computation.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Topological Methods in Data Analysis and Visualization IIIClear and Compress: Computing Persistent Homology in Chunks

Part of the Mathematics and Visualization Book Series
Editors: Bremer, Peer-Timo; Hotz, Ingrid; Pascucci, Valerio; Peikert, Ronald
Bauer, Ulrich; Kerber, Michael; Reininghaus, Jan
Topological Methods in Data Analysis and Visualization III — Mar 19, 2014
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References (19)

Publisher
Springer International Publishing
Copyright
© Springer International Publishing Switzerland 2014
ISBN
978-3-319-04098-1
Pages
103–117
DOI
10.1007/978-3-319-04099-8_7
Publisher site
See Chapter on Publisher Site

Abstract

[We present a parallel algorithm for computing the persistent homology of a filtered chain complex. Our approach differs from the commonly used reduction algorithm by first computing persistence pairs within local chunks, then simplifying the unpaired columns, and finally applying standard reduction on the simplified matrix. The approach generalizes a technique by Günther et al., which uses discrete Morse Theory to compute persistence; we derive the same worst-case complexity bound in a more general context. The algorithm employs several practical optimization techniques, which are of independent interest. Our sequential implementation of the algorithm is competitive with state-of-the-art methods, and we further improve the performance through parallel computation.]

Published: Mar 19, 2014

Keywords: Betti Number; Cubical Complex; Chunk Size; Column Operation; Boundary Matrix

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