Graphcode: Learning from multiparameter persistent homology using graph neural networks

• URL: http://arxiv.org/abs/2405.14302v1
• Date: Thu, 23 May 2024 08:22:00 GMT
• Title: Graphcode: Learning from multiparameter persistent homology using graph neural networks
• Authors: Michael Kerber, Florian Russold,
• Abstract summary: Graphcodes handle datasets that are filtered along two real-valued scale parameters. Graphcodes yield an informative and interpretable summary. They can be readily integrated in machine learning pipelines using graph neural networks.
• Score: 0.06138671548064355
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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