Graphcode: Learning from multiparameter persistent homology using graph neural networks
This provides a more efficient and interpretable method for analyzing multi-parameter topological data, benefiting researchers in computational topology and machine learning.
The authors tackled the challenge of summarizing multi-parameter topological data by introducing graphcodes, a novel multi-scale summary based on persistent homology, which achieved better classification accuracy than state-of-the-art approaches on various datasets.
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.