The Compressed Annotation Matrix: An Efficient Data Structure for Computing Persistent Cohomology
Algorithmica(2015)
摘要
Persistent homology with coefficients in a field 𝔽 coincides with the same for cohomology because of duality. We propose an implementation of a recently introduced algorithm for persistent cohomology that attaches annotation vectors with the simplices. We separate the representation of the simplicial complex from the representation of the cohomology groups, and introduce a new data structure for maintaining the annotation matrix, which is more compact and reduces substantially the amount of matrix operations. In addition, we propose a heuristic to simplify further the representation of the cohomology groups and improve both time and space complexities. The paper provides a theoretical analysis, as well as a detailed experimental study of our implementation and comparison with state-of-the-art software for persistent homology and cohomology.
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关键词
Persistent cohomology,Annotation,Data structure,Simplicial complex,Algorithm,Implementation
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