Network Lasso: Clustering and Optimization in Large Graphs

Convex optimization is an essential tool for modern data analysis, as it provides a framework to formulate and solve many problems in machine learning and data mining. However, general convex op-timization solvers do not scale well, and scalable solvers are often specialized to only work on a narrow class of problems. There-fore, there is a need for simple, scalable algorithms that can solve many common optimization problems. In this paper, we introduce the network lasso, a generalization of the group lasso to a network setting that allows for simultaneous clustering and optimization on graphs. We develop an algorithm based on the Alternating Direc-tion Method of Multipliers (ADMM) to solve this problem in a dis-tributed and scalable manner, which allows for guaranteed global convergence even on large graphs. We also examine a non-convex extension of this approach. We then demonstrate that many types of problems can be expressed in our framework. We focus on three in particular — binary classification, predicting housing prices, and event detection in time series data — comparing the network lasso to baseline approaches and showing that it is both a fast and accu-rate method of solving large optimization problems