Graphcode: Learning from multiparameter persistent homology using graph neural networks
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929354816094208 |
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| author | Kerber, Michael Russold, Florian |
| author_facet | Kerber, Michael Russold, Florian |
| contents | We introduce graphcodes, a novel multi-scale summary of the topological properties of a dataset that is based on the well-established theory of persistent homology. Graphcodes handle datasets that are filtered along two real-valued scale parameters. Such multi-parameter topological summaries are usually based on complicated theoretical foundations and difficult to compute; in contrast, graphcodes yield an informative and interpretable summary and can be computed as efficient as one-parameter summaries. Moreover, a graphcode is simply an embedded graph and can therefore be readily integrated in machine learning pipelines using graph neural networks. We describe such a pipeline and demonstrate that graphcodes achieve better classification accuracy than state-of-the-art approaches on various datasets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_14302 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Graphcode: Learning from multiparameter persistent homology using graph neural networks Kerber, Michael Russold, Florian Algebraic Topology Machine Learning We introduce graphcodes, a novel multi-scale summary of the topological properties of a dataset that is based on the well-established theory of persistent homology. Graphcodes handle datasets that are filtered along two real-valued scale parameters. Such multi-parameter topological summaries are usually based on complicated theoretical foundations and difficult to compute; in contrast, graphcodes yield an informative and interpretable summary and can be computed as efficient as one-parameter summaries. Moreover, a graphcode is simply an embedded graph and can therefore be readily integrated in machine learning pipelines using graph neural networks. We describe such a pipeline and demonstrate that graphcodes achieve better classification accuracy than state-of-the-art approaches on various datasets. |
| title | Graphcode: Learning from multiparameter persistent homology using graph neural networks |
| topic | Algebraic Topology Machine Learning |
| url | https://arxiv.org/abs/2405.14302 |