Efficient Network Embedding by Approximate Equitable Partitions

TL;DR

This paper presents a fast, scalable network embedding method based on approximate equitable partitions, enabling efficient analysis of large networks while maintaining high performance in various tasks.

Contribution

It introduces a novel approximate equitable partition technique with a tunable parameter, improving scalability and efficiency over existing methods.

Findings

Comparable or superior performance in visualization, classification, and regression tasks.

Significantly reduced computational cost, up to three orders of magnitude.

Effective embedding of large-scale networks previously difficult to handle.

Abstract

Structural network embedding is a crucial step in enabling effective downstream tasks for complex systems that aims to project a network into a lower-dimensional space while preserving similarities among nodes. We introduce a simple and efficient embedding technique based on approximate variants of equitable partitions. The approximation consists in introducing a user-tunable tolerance parameter relaxing the otherwise strict condition for exact equitable partitions that can be hardly found in real-world networks. We exploit a relationship between equitable partitions and equivalence relations for Markov chains and ordinary differential equations to develop a partition refinement algorithm for computing an approximate equitable partition in polynomial time. We compare our method against state-of-the-art embedding techniques on benchmark networks. We report comparable -- when not superior -- performance for visualization, classification, and regression tasks at a cost between one and three orders of magnitude smaller using a prototype implementation, enabling the embedding of large-scale networks which could not be efficiently handled by most of the competing techniques.