Efficient Network Embedding by Approximate Equitable Partitions
This work addresses the need for scalable embedding methods for large-scale networks, offering a practical solution for researchers and practitioners dealing with complex systems, though it is incremental in improving efficiency over existing techniques.
The paper tackles the problem of structural network embedding for complex systems by introducing an efficient technique based on approximate equitable partitions, achieving comparable or superior performance in tasks like visualization and classification with a cost reduction of 1-3 orders of magnitude.
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.