Graphcode: Learning from multiparameter persistent homology using graph neural networks
<|reference_start|>Graphcode: Learning from multiparameter persistent homology using graph neural networks: 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.<|reference_end|>
@article{kerber2024graphcode:,
    title={Graphcode: Learning from multiparameter persistent homology using graph
  neural networks},
    author={Michael Kerber, Florian Russold},
    journal={arXiv preprint arXiv:2405.14302},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.14302},
    primaryClass={math.AT cs.LG}
}