Graphcode: Learning from multiparameter persistent homology using graph neural networks
Florian Russold, Michael Kerber
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.
BibTeX
@inproceedings{
russold2024graphcode,
title={Graphcode: Learning from multiparameter persistent homology using graph neural networks},
author={Florian Russold and Michael Kerber},
booktitle={The Thirty-eighth Annual Conference on Neural Information Processing Systems},
year={2024},
url={https://openreview.net/forum?id=O23XfTnhWR}
}