Graphcode: Learning from Multiparameter Persistent Homology Using Graph Neural Networks
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.
Cite
Text
Kerber and Russold. "Graphcode: Learning from Multiparameter Persistent Homology Using Graph Neural Networks." Neural Information Processing Systems, 2024. doi:10.52202/079017-1300Markdown
[Kerber and Russold. "Graphcode: Learning from Multiparameter Persistent Homology Using Graph Neural Networks." Neural Information Processing Systems, 2024.](https://mlanthology.org/neurips/2024/kerber2024neurips-graphcode/) doi:10.52202/079017-1300BibTeX
@inproceedings{kerber2024neurips-graphcode,
title = {{Graphcode: Learning from Multiparameter Persistent Homology Using Graph Neural Networks}},
author = {Kerber, Michael and Russold, Florian},
booktitle = {Neural Information Processing Systems},
year = {2024},
doi = {10.52202/079017-1300},
url = {https://mlanthology.org/neurips/2024/kerber2024neurips-graphcode/}
}