Graphcode: Learning from multiparameter persistent homology using graph neural networks

TL;DR

Graphcodes are a new multi-scale topological summary based on multiparameter persistent homology, designed for efficient computation and integration with graph neural networks, leading to improved classification accuracy.

Contribution

Introduction of graphcodes, a novel multi-parameter topological summary that is interpretable, computationally efficient, and compatible with graph neural networks for machine learning tasks.

Findings

Graphcodes outperform state-of-the-art methods in classification accuracy.

They are efficiently computed and easily integrated into existing machine learning pipelines.

Graphcodes provide an interpretable topological summary for datasets with two scale parameters.

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.