首页|Computing Persistent Homology by Spanning Trees and Critical Simplices

Computing Persistent Homology by Spanning Trees and Critical Simplices

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Topological data analysis can extract effective information from higher-dimensional data.Its mathematical basis is persistent homology.The persistent homology can calculate topological features at different spatiotemporal scales of the dataset,that is,establishing the integrated taxonomic relation among points,lines,and simplices.Here,the simplicial network composed of all-order simplices in a simplicial complex is essential.Because the sequence of nested simplicial subnetworks can be regarded as a discrete Morse function from the simplicial network to real values,a method based on the concept of critical simplices can be developed by searching all-order spanning trees.Employing this new method,not only the Morse function values with the theoretical minimum number of critical simplices can be obtained,but also the Betti numbers and composition of all-order cavities in the simplicial network can be calculated quickly.Finally,this method is used to analyze some examples and compared with other methods,showing its effectiveness and feasibility.

Dinghua Shi、Zhifeng Chen、Chuang Ma、Guanrong Chen

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Department of Mathematics,College of Science,Shanghai University,Shanghai,China

School of Big Data,Fuzhou University of International Studies and Trade,Fuzhou,China

Department of Data Science and Big Data Technology,School of Internet,Anhui University,Hefei,China

Department of Electrical Engineering,City University of Hong Kong,Hong Kong,China

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National Natural Science Foundation of ChinaNational Natural Science Foundation of China

6217309512005001

2024

10.34133/research.0230

研究(英文)

研究(英文)

CSTPCD
ISSN：
年,卷(期)：2024.2024(2)
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