Two-dimensional Fused Matrix Logistic Regression Model Optimization Method

With the rapid development of modern science and technology,a large number of matrix data with complex structures emerge,and there is an increasing number of ma-trix classification data with the low rank and the sparsity of adjacent row differences and adjacent column differences.Logistic regression is an important classification al-gorithm.However,the existing regularized logistic regression model cannot handle this specific structure of the data well.Based on this reason,in this article we first propose a two-dimensional（2D）Fused matrix logistic regression model.The model contains a nuclear norm regularization and two Fused Lasso regularizations in matrix form which are used to constrain the low rank of the matrix and the sparsity of adjacent row d-ifferences and adjacent column differences.In statistical properties,we establish the consistency of the estimator of the two-dimensional Fused matrix logistic regression model coefficient matrix,which prove the feasibility and effectiveness of the model.In algorithm design,considering the high computational cost of high-dimensional matrix inversion,from the perspective of duality,we design an efficeint symmetric Guass-Sediel alternating direction method of multipliers（s GS-ADMM）algorithm to solve the problem.For each subproblem of the iterative step,a closed-form solution can be ob-tained or obtained by an algorithm.In addition,we give the global convergence and Q-linear convergence of the algorithm.Finally,the numerical experiments on simula-tion and real datasets show that the 2DFMLR has superior performance in estimation and prediction compared with matrix logistic regression with nuclear norm penalty and vectorized l₁-norm penalty respectively.