Matroid Filtrations and Computational Persistent Homology
نویسندگان
چکیده
This technical report introduces a novel approach to efficient computation in homological algebra over fields, with particular emphasis on computing the persistent homology of a filtered topological cell complex. The algorithms here presented rely on a novel relationship between discrete Morse theory, matroid theory, and classical matrix factorizations. We provide background, detail the algorithms, and benchmark the software implementation in the EIRENE package.
منابع مشابه
Morse Theory for Filtrations and Efficient Computation of Persistent Homology
We introduce an efficient preprocessing algorithm to reduce the number of cells in a filtered cell complex while preserving its persistent homology groups. The technique is based on an extension of combinatorial Morse theory from complexes to filtrations.
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تاریخ انتشار 2016