Filtration Curves for Graph Representation

Leslie O'Bray, Bastian Rieck, Karsten Borgwardt

Abstract:

The two predominant approaches to graph comparison in recent years are based on (i) enumerating matching subgraphs or (ii) comparing neighborhoods of nodes. In this work, we complement these
two perspectives with a third way of representing graphs: using filtration curves from topological data analysis that capture both edge weight information and global graph structure. Filtration curves
are highly efficient to compute and lead to expressive representations of graphs, which we demonstrate on graph classification benchmark datasets. Our work opens the door to a new form of graph representation in data mining.