2021/06/13 by Bongsoo Yi, Kevin O’Connor, Yi, Bongsoo +5 · 1 citation
Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Markov Chains and Monte Carlo Methods #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2106.07106
openalex publication_date 2021/06/13 · openalex created_date 2023/01/06 · openalex updated_date 2026/07/28
We describe and study a transport based procedure called NetOTC (network optimal transition coupling) for the comparison and alignment of two networks. The networks of interest may be directed or undirected, weighted or unweighted, and may have distinct vertex sets of different sizes. Given two networks and a cost function relating their vertices, NetOTC finds a transition coupling of their associated random walks having minimum expected cost. The minimizing cost quantifies the difference between the networks, while the optimal transport plan itself provides alignments of both the vertices and the edges of the two networks. Coupling of the full random walks, rather than their marginal distributions, ensures that NetOTC captures local and global information about the networks, and preserves edges. NetOTC has no free parameters, and does not rely on randomization. We investigate a number of theoretical properties of NetOTC and present experiments establishing its empirical performance.