Feature-enriched hyperbolic network geometry

TL;DR

This paper introduces a hyperbolic geometric framework for modeling graph data with features, revealing complex node-feature relationships and aiding in understanding GCNs' inner workings.

Contribution

It presents a novel hyperbolic space model that integrates node features into graph geometry, enhancing analysis of topological and feature-based correlations.

Findings

Identifies correlations between nodes and features in real data

Generates synthetic datasets mimicking real topological properties

Provides insights into the structure of GCNs

Abstract

Graph-structured data provide a comprehensive description of complex systems, encompassing not only the interactions among nodes but also the intrinsic features that characterize these nodes. These features play a fundamental role in the formation of links within the network, making them valuable for extracting meaningful topological information. Notably, features are at the core of deep learning techniques such as Graph Convolutional Neural Networks (GCNs) and offer great utility in tasks like node classification, link prediction, and graph clustering. In this paper, we present a comprehensive framework that treats features as tangible entities and establishes a bipartite graph connecting nodes and features. By assuming that nodes sharing similarities should also share features, we introduce a hyperbolic geometric space where both nodes and features coexist, shaping the structure of both the node network and the bipartite network of nodes and features. Through this framework, we can identify correlations between nodes and features in real data and generate synthetic datasets that mimic the topological properties of their connectivity patterns. The approach provides insights into the inner workings of GCNs by revealing the intricate structure of the data.