A novel approach to graph distinction through GENEOs and permutants

TL;DR

This paper explores the use of Group Equivariant Non-Expansive Operators (GENEOs) for distinguishing r-regular graphs up to isomorphism, demonstrating their efficiency, interpretability, and potential as a general-purpose tool in machine learning.

Contribution

It introduces the application of GENEOs to graph isomorphism problems, showcasing their effectiveness and interpretability in structural data comparison.

Findings

GENEOs effectively distinguish r-regular graphs

They offer a good balance between efficiency and computational cost

Actions of GENEOs on data are easily interpretable

Abstract

The theory of Group Equivariant Non-Expansive Operators (GENEOs) was initially developed in Topological Data Analysis for the geometric approximation of data observers, including their invariances and symmetries. This paper departs from that line of research and explores the use of GENEOs for distinguishing $r$-regular graphs up to isomorphisms. In doing so, we aim to test the capabilities and flexibility of these operators. Our experiments show that GENEOs offer a good compromise between efficiency and computational cost in comparing $r$-regular graphs, while their actions on data are easily interpretable. This supports the idea that GENEOs could be a general-purpose approach to discriminative problems in Machine Learning when some structural information about data and observers is explicitly given.