View a PDF of the paper titled Efficient Network Embedding by Approximate Equitable Partitions, by Giuseppe Squillace and 3 other authors
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.
Submission history
From: Giuseppe Squillace [view email]
[v1]
Mon, 16 Sep 2024 10:51:24 UTC (1,590 KB)
[v2]
Thu, 19 Dec 2024 21:21:49 UTC (1,510 KB)
Source link
lol