# An Algorithm for Graph-Fused Lasso Based on Graph Decomposition

## TL;DR

This paper introduces a novel graph-fused lasso algorithm that decomposes the objective function to improve computational efficiency and convergence speed using ADMM.

## Contribution

It proposes a new decomposition approach for the GFL objective function, enhancing efficiency over existing network lasso methods.

## Key findings

- Faster convergence in simulations compared to network lasso.
- Lower computational cost per iteration.
- Effective in parameter estimation with graph-structured data.

## Abstract

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