On the Duality Between Network Flows and Network Lasso

• Published in: IEEE signal processing letters Vol. 27; pp. 940 - 944
• Main Author: Jung, Alexander
• Format: Journal Article
• Language: English
• Published: New York IEEE 2020; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Big data applications; Clustering; Clustering algorithms; compressed sensing; Data models; Linear programming; Machine learning; machine learning algorithms; Minimization; networks; Optimization; optimization methods; Signal processing algorithms; Social networks
• ISSN: 1070-9908; 1558-2361
• DOI: 10.1109/LSP.2020.2998400

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 the 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.