2D Fused Matrix Regression

In this era of data explosion,the data structures are becoming more complex.In this paper,we consider the situation where the data structure are matrix with both lowrank and sparsity in the difference of successive rows and columns.To meet these needs of data structure,we propose a new two-dimensional(2D)Fused matrix regression model.Then,we establish the risk bound of the proposed model.Moreover,we develop an efficient symmetric Gauss-Seidel based alternating direction method of multipliers(s GS-ADMM)algorithm to solve the 2D Fused matrix regression model,and also show the global convergence of the proposed algorithm.Finally,experimental results of simulation and real data show that our method performs better in estimation and prediction.