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The network Lasso is a recently proposed convex optimization method formachine learning from massive network structured datasets, i.e., big data overnetworks. It is a variant of the well-known least absolute shrinkage andselection operator (Lasso), which is underlying many methods in learning andsignal processing involving sparse models. Highly scalable implementations ofthe network Lasso can be obtained by state-of-the art proximal methods, e.g.,the alternating direction method of multipliers (ADMM). By generalizing theconcept of the compatibility condition put forward by van de Geer and Buehlmannas a powerful tool for the analysis of plain Lasso, we derive a sufficientcondition, i.e., the network compatibility condition, on the underlying networktopology such that network Lasso accurately learns a clustered underlying graphsignal. This network compatibility condition relates the location of thesampled nodes with the clustering structure of the network. In particular, theNCC informs the choice of which nodes to sample, or in machine learning terms,which data points provide most information if labeled.

Recovery Conditions and Sampling Strategies for Network Lasso