On the Duality between Network Flows and Network Lasso
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The data arising in many application domains have an intrinsic network structure. Such network structure is computationally apprealing due to the availability of highly scalable graph algorithms. An important class of graph algorithms is related to optimizing network flows. This paper explores the duality of network flow methods and the recently proposed network Lasso. Network Lasso extends the Lasso method from sparse linear models to clustered graph signals. It turns out that the computational and statistical properties of network Lasso crucially depends on the existence of sufficiently large network flows. Using elementary tools from convex analysis, we offer a precise characterization of the duality between network Lasso and a minimum cost network flow problem. This duality provides a strong link between network Lasso methods and network flow algorithms.
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