Li M, Guo Q, Zhai W J, Chen B Z
School of Science, Beijing Jiaotong University, Beijing, People's Republic of China.
Department of Mathematics, Beijing Jiaotong University Haibin College, Cangzhou, People's Republic of China.
J Appl Stat. 2020 Mar 18;47(13-15):2623-2640. doi: 10.1080/02664763.2020.1742296. eCollection 2020.
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.
具有矩阵和向量形式的数据集在现代科学领域越来越受欢迎。基于数据集的结构，需要估计矩阵和向量系数。目前，已经提出了矩阵回归模型，它们主要关注没有向量变量的矩阵。为了充分探索数据集的复杂结构，我们提出了一种新颖的矩阵回归模型，该模型结合了融合LASSO和核范数惩罚，它可以同时处理包含矩阵和向量变量的数据。我们的主要工作是设计一种高效算法来求解所提出的低秩和融合LASSO矩阵回归模型。按照现有的思路，我们设计了线性化交替方向乘子法并建立了其全局收敛性。最后，我们进行数值实验来证明我们方法的有效性。特别是，我们将我们的模型应用于两个真实数据集，即信号形状和部分轨迹的行程时间预测。
