A novel approach to graph distinction through GENEOs and permutants
Abstract The theory of Group Equivariant Non-Expansive Operators (GENEOs) was initially developed in Topological Data Analysis for the geometric approximation of data observers, including their invariances and symmetries. This paper departs from that line of research and explores the use of GENEOs f...
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2025-02-01
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| Series: | Scientific Reports |
| Online Access: | https://doi.org/10.1038/s41598-025-90152-7 |
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| _version_ | 1850190767596765184 |
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| author | Giovanni Bocchi Massimo Ferri Patrizio Frosini |
| author_facet | Giovanni Bocchi Massimo Ferri Patrizio Frosini |
| author_sort | Giovanni Bocchi |
| collection | DOAJ |
| description | Abstract The theory of Group Equivariant Non-Expansive Operators (GENEOs) was initially developed in Topological Data Analysis for the geometric approximation of data observers, including their invariances and symmetries. This paper departs from that line of research and explores the use of GENEOs for distinguishing r-regular graphs up to isomorphisms. In doing so, we aim to test the capabilities and flexibility of these operators. Our experiments show that GENEOs offer a good compromise between efficiency and computational cost in comparing r-regular graphs, while their actions on data are easily interpretable. This supports the idea that GENEOs could be a general-purpose approach to discriminative problems in Machine Learning when some structural information about data and observers is explicitly given. |
| format | Article |
| id | doaj-art-c68ca7e3d01a45dda38032ca2b36a2b5 |
| institution | OA Journals |
| issn | 2045-2322 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj-art-c68ca7e3d01a45dda38032ca2b36a2b52025-08-20T02:15:11ZengNature PortfolioScientific Reports2045-23222025-02-0115111110.1038/s41598-025-90152-7A novel approach to graph distinction through GENEOs and permutantsGiovanni Bocchi0Massimo Ferri1Patrizio Frosini2Department of Environmental Science and Policy, University of MilanDepartment of Mathematics and ARCES, University of BolognaDepartment of Computer Science, University of PisaAbstract The theory of Group Equivariant Non-Expansive Operators (GENEOs) was initially developed in Topological Data Analysis for the geometric approximation of data observers, including their invariances and symmetries. This paper departs from that line of research and explores the use of GENEOs for distinguishing r-regular graphs up to isomorphisms. In doing so, we aim to test the capabilities and flexibility of these operators. Our experiments show that GENEOs offer a good compromise between efficiency and computational cost in comparing r-regular graphs, while their actions on data are easily interpretable. This supports the idea that GENEOs could be a general-purpose approach to discriminative problems in Machine Learning when some structural information about data and observers is explicitly given.https://doi.org/10.1038/s41598-025-90152-7 |
| spellingShingle | Giovanni Bocchi Massimo Ferri Patrizio Frosini A novel approach to graph distinction through GENEOs and permutants Scientific Reports |
| title | A novel approach to graph distinction through GENEOs and permutants |
| title_full | A novel approach to graph distinction through GENEOs and permutants |
| title_fullStr | A novel approach to graph distinction through GENEOs and permutants |
| title_full_unstemmed | A novel approach to graph distinction through GENEOs and permutants |
| title_short | A novel approach to graph distinction through GENEOs and permutants |
| title_sort | novel approach to graph distinction through geneos and permutants |
| url | https://doi.org/10.1038/s41598-025-90152-7 |
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