Alignment and Comparison of Directed Networks via Transition Couplings of Random Walks
This method addresses network alignment for researchers in fields like bioinformatics or social network analysis, offering a parameter-free approach that captures both local and global information, though it appears incremental as an extension of optimal transport to network contexts.
The authors tackled the problem of comparing and aligning two networks with potentially different sizes and types by introducing NetOTC, a transport-based method that finds an optimal transition coupling of random walks to minimize expected cost, which quantifies network differences and provides vertex and edge alignments.
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.