Triangle Lasso for Simultaneous Clustering and Optimization in Graph Datasets

Recently, network lasso has dawn much attention due to its remarkable performance on simultaneous clustering and optimization. However, it usually suffers from the imperfect data (noise, missing values, etc.), and yields sub-optimal solutions. The reason is that it finds the similar instances according to their features directly, which is usually impacted by the imperfect data, and thus returns sub-optimal results. In this paper, we propose triangle lasso to avoid its disadvantage for graph datasets. In a graph dataset, each instance is represented by a vertex. If two instances have many common adjacent vertices, they tend to become similar. Although some instances are profiled by the imperfect data, it is still able to find the similar counterparts. Furthermore, we develop an efficient algorithm based on Alternating Direction Method of Multipliers (ADMM) to obtain a moderately accurate solution. In addition, we present a dual method to obtain the accurate solution with the low additional time consumption. We demonstrate through extensive numerical experiments that triangle lasso is robust to the imperfect data. It usually yields a better performance than the state-of-the-art method when performing data analysis tasks in practical scenarios.