Persistent Homology and Graphs Representation Learning

TL;DR

This paper explores how persistent homology can analyze and extract topological features from node embeddings in graphs, providing a new persistence-based graph descriptor applicable to various embedding algorithms.

Contribution

It introduces a novel topological descriptor derived from persistent homology for node embeddings, applicable to multiple graph representation methods.

Findings

Topological descriptors effectively characterize node embeddings.

The method distinguishes different embedding algorithms based on topological features.

Persistent homology provides a robust tool for analyzing graph representations.

Abstract

This article aims to study the topological invariant properties encoded in node graph representational embeddings by utilizing tools available in persistent homology. Specifically, given a node embedding representation algorithm, we consider the case when these embeddings are real-valued. By viewing these embeddings as scalar functions on a domain of interest, we can utilize the tools available in persistent homology to study the topological information encoded in these representations. Our construction effectively defines a unique persistence-based graph descriptor, on both the graph and node levels, for every node representation algorithm. To demonstrate the effectiveness of the proposed method, we study the topological descriptors induced by DeepWalk, Node2Vec and Diff2Vec.