On the Expressivity of Persistent Homology in Graph Learning
This work addresses a gap in graph machine learning for researchers, but it is incremental as it builds on existing empirical findings without introducing a new method.
The paper tackles the lack of theoretical understanding of persistent homology in graph learning by providing an introduction and analyzing its expressivity, showing improved predictive performance for datasets like molecules through multi-scale topological descriptors.
Persistent homology, a technique from computational topology, has recently shown strong empirical performance in the context of graph classification. Being able to capture long range graph properties via higher-order topological features, such as cycles of arbitrary length, in combination with multi-scale topological descriptors, has improved predictive performance for data sets with prominent topological structures, such as molecules. At the same time, the theoretical properties of persistent homology have not been formally assessed in this context. This paper intends to bridge the gap between computational topology and graph machine learning by providing a brief introduction to persistent homology in the context of graphs, as well as a theoretical discussion and empirical analysis of its expressivity for graph learning tasks.