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This work proposes a new algorithm for solving the graph-fused lasso (GFL), amethod for parameter estimation that operates under the assumption that thesignal tends to be locally constant over a predefined graph structure. Theproposed method applies the alternating direction method of multipliers (ADMM)algorithm and is based on the decomposition of the objective function into twocomponents. While ADMM has been widely used in this problem, existing workssuch as network lasso decompose the objective function into the loss functioncomponent and the total variation penalty component. In comparison, this workproposes to decompose the objective function into two components, where onecomponent is the loss function plus part of the total variation penalty, andthe other component is the remaining total variation penalty. Compared with thenetwork lasso algorithm, this method has a smaller computational cost periteration and converges faster in most simulations numerically.

An Algorithm for Graph-Fused Lasso Based on Graph Decomposition