PERSISTENT DIRECTED FLAG LAPLACIAN
Topological data analysis (TDA) has had enormous success in science and engineering in the past decade. Persistent topological Laplacians (PTLs) overcome some limitations of persistent homology, a key technique in TDA, and provide substantial insight to the behavior of various geometric and topologi...
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| Published in: | Foundations of data science Vol. 7; no. 3; p. 737 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
United States
01.09.2025
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| Subjects: | |
| ISSN: | 2639-8001, 2639-8001 |
| Online Access: | Get more information |
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| Summary: | Topological data analysis (TDA) has had enormous success in science and engineering in the past decade. Persistent topological Laplacians (PTLs) overcome some limitations of persistent homology, a key technique in TDA, and provide substantial insight to the behavior of various geometric and topological objects. This work extends PTLs to directed flag complexes, which are an exciting generalization to flag complexes, also known as clique complexes, that arise naturally in many situations. We introduce the directed flag Laplacian and show that the proposed persistent directed flag Laplacian (PDFL) is a distinct way of analyzing these flag complexes. Example calculations are provided to demonstrate the potential of the proposed PDFL in real world applications. |
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| Bibliography: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 |
| ISSN: | 2639-8001 2639-8001 |
| DOI: | 10.3934/fods.2024048 |