The linearized alternating direction method of multipliers for low-rank and fused LASSO matrix regression model.

Datasets with matrix and vector form are increasingly popular in modern scientific fields. Based on structures of datasets, matrix and vector coefficients need to be estimated. At present, the matrix regression models were proposed, and they mainly focused on the matrix without vector variables. In order to fully explore complex structures of datasets, we propose a novel matrix regression model which combines fused LASSO and nuclear norm penalty, which can deal with the data containing matrix and vector variables meanwhile. Our main work is to design an efficient algorithm to solve the proposed low-rank and fused LASSO matrix regression model. Following the existing idea, we design the linearized alternating direction method of multipliers and establish its global convergence. Finally, we carry out numerical experiments to demonstrate the efficiency of our method. Especially, we apply our model to two real datasets, i.e. the signal shapes and the trip time prediction from partial trajectories.