TL;DR
This paper introduces a row reduction algorithm for computing barcode decompositions in persistence modules, emphasizing symmetry and optimization techniques to improve understanding and efficiency.
Contribution
It presents a novel row reduction algorithm that dualizes standard persistence methods and clarifies the symmetry between clear and compress optimizations.
Findings
Algorithm effectively computes barcode decompositions.
Highlights symmetry between optimization techniques.
Improves understanding of persistence module computations.
Abstract
We present a row reduction algorithm to compute the barcode decomposition of persistence modules. This algorithm dualises the standard persistence one and clarifies the symmetry between clear and compress optimisations.
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Taxonomy
TopicsTopological and Geometric Data Analysis · Cell Image Analysis Techniques · Data Visualization and Analytics