A cohomology-based Gromov–Hausdorff metric approach for quantifying molecular similarity
Abstract We introduce a cohomology-based Gromov–Hausdorff ultrametric method to analyze 1-dimensional and higher-dimensional (co)homology groups, focusing on loops, voids, and higher-dimensional cavity structures in simplicial complexes, to address typical clustering questions arising in molecular d...
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2025-03-01
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| Series: | Scientific Reports |
| Online Access: | https://doi.org/10.1038/s41598-025-93381-y |
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| author | JunJie Wee Xue Gong Wilderich Tuschmann Kelin Xia |
| author_facet | JunJie Wee Xue Gong Wilderich Tuschmann Kelin Xia |
| author_sort | JunJie Wee |
| collection | DOAJ |
| description | Abstract We introduce a cohomology-based Gromov–Hausdorff ultrametric method to analyze 1-dimensional and higher-dimensional (co)homology groups, focusing on loops, voids, and higher-dimensional cavity structures in simplicial complexes, to address typical clustering questions arising in molecular data analysis. The Gromov–Hausdorff distance quantifies the dissimilarity between two metric spaces. In this framework, molecules are represented as simplicial complexes, and their cohomology vector spaces are computed to capture intrinsic topological invariants encoding loop and cavity structures. These vector spaces are equipped with a suitable distance measure, enabling the computation of the Gromov–Hausdorff ultrametric to evaluate structural dissimilarities. We demonstrate the methodology using organic–inorganic halide perovskite (OIHP) structures. The results highlight the effectiveness of this approach in clustering various molecular structures. By incorporating geometric information, our method provides deeper insights compared to traditional persistent homology techniques. |
| format | Article |
| id | doaj-art-0a600d859adf461fbe1d5d0a528eb405 |
| institution | DOAJ |
| issn | 2045-2322 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj-art-0a600d859adf461fbe1d5d0a528eb4052025-08-20T02:49:30ZengNature PortfolioScientific Reports2045-23222025-03-0115111110.1038/s41598-025-93381-yA cohomology-based Gromov–Hausdorff metric approach for quantifying molecular similarityJunJie Wee0Xue Gong1Wilderich Tuschmann2Kelin Xia3Department of Mathematics, Michigan State UniversityDivision of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological UniversityInstitut für Algebra und Geometrie, Arbeitsgruppe Differentialgeometrie, Karlsruher Institut für TechnologieDivision of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological UniversityAbstract We introduce a cohomology-based Gromov–Hausdorff ultrametric method to analyze 1-dimensional and higher-dimensional (co)homology groups, focusing on loops, voids, and higher-dimensional cavity structures in simplicial complexes, to address typical clustering questions arising in molecular data analysis. The Gromov–Hausdorff distance quantifies the dissimilarity between two metric spaces. In this framework, molecules are represented as simplicial complexes, and their cohomology vector spaces are computed to capture intrinsic topological invariants encoding loop and cavity structures. These vector spaces are equipped with a suitable distance measure, enabling the computation of the Gromov–Hausdorff ultrametric to evaluate structural dissimilarities. We demonstrate the methodology using organic–inorganic halide perovskite (OIHP) structures. The results highlight the effectiveness of this approach in clustering various molecular structures. By incorporating geometric information, our method provides deeper insights compared to traditional persistent homology techniques.https://doi.org/10.1038/s41598-025-93381-y |
| spellingShingle | JunJie Wee Xue Gong Wilderich Tuschmann Kelin Xia A cohomology-based Gromov–Hausdorff metric approach for quantifying molecular similarity Scientific Reports |
| title | A cohomology-based Gromov–Hausdorff metric approach for quantifying molecular similarity |
| title_full | A cohomology-based Gromov–Hausdorff metric approach for quantifying molecular similarity |
| title_fullStr | A cohomology-based Gromov–Hausdorff metric approach for quantifying molecular similarity |
| title_full_unstemmed | A cohomology-based Gromov–Hausdorff metric approach for quantifying molecular similarity |
| title_short | A cohomology-based Gromov–Hausdorff metric approach for quantifying molecular similarity |
| title_sort | cohomology based gromov hausdorff metric approach for quantifying molecular similarity |
| url | https://doi.org/10.1038/s41598-025-93381-y |
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