KOO Method-based Consistent Clustering for Group-wise Linear Regression with Graph Structure

The kick-one-out (KOO) method is a variable selection method based on a model selection criterion. The method is very simple, and yet it has consistency in variable selection under a high-dimensional asymptotic framework with a specific model selection criterion. This paper proposes the join-twotogether (JTT) method, which is a clustering method based on the KOO method for group-wise linear regression with graph structure. The JTT method formulates the clustering problem as an edge selection problem for a graph and determines whether to select each edge based on the KOO method. We can employ network Lasso to perform such a clustering. However, network Lasso is somewhat cumbersome because there is no good algorithm for solving the associated optimization problem and the tuning is complicated. Therefore, by deriving a model selection criterion such that the JTT method has consistency in clustering under a high-dimensional asymptotic framework, we propose a simple yet powerful method that outperforms network Lasso.