On the Duality between Network Flows and Network Lasso
This provides a theoretical link between nLasso methods and graph algorithms, potentially aiding in applications like time series or social network analysis, but it is incremental as it builds on existing nLasso work.
The paper tackles the problem of joint clustering and optimization for networked data by establishing a duality between network Lasso (nLasso) and network flow optimization, showing that nLasso is equivalent to a minimum-cost flow problem and characterizing solutions via network flows.
Many applications generate data with an intrinsic network structure such as time series data, image data or social network data. The network Lasso (nLasso) has been proposed recently as a method for joint clustering and optimization of machine learning models for networked data. The nLasso extends the Lasso from sparse linear models to clustered graph signals. This paper explores the duality of nLasso and network flow optimization. We show that, in a very precise sense, nLasso is equivalent to a minimum-cost flow problem on the data network structure. Our main technical result is a concise characterization of nLasso solutions via existence of certain network flows. The main conceptual result is a useful link between nLasso methods and basic graph algorithms such as clustering or maximum flow.