Graph Filtration Learning

TL;DR

This paper introduces a novel graph readout method using learnable persistent homology for graph classification, demonstrating improved performance especially when graph structure is informative.

Contribution

It presents a new differentiable readout operation based on persistent homology, enabling better graph-level representations in learning tasks.

Findings

Outperforms previous graph readout techniques

Effective when graph connectivity is informative

Provides a differentiable approach to persistent homology

Abstract

We propose an approach to learning with graph-structured data in the problem domain of graph classification. In particular, we present a novel type of readout operation to aggregate node features into a graph-level representation. To this end, we leverage persistent homology computed via a real-valued, learnable, filter function. We establish the theoretical foundation for differentiating through the persistent homology computation. Empirically, we show that this type of readout operation compares favorably to previous techniques, especially when the graph connectivity structure is informative for the learning problem.