The LADMM Method For Block And Low-rank Matrix Regression

With the development of modern science and technology,conforming to the big data era,Matrix regression is a common problem in scientific research and practical ap-plications,such as machine learning and artificial intelligence,gene expression analysis,brain neural networks and so on.The data types related to matrix regression problem-s are complex and have the characteristics of diversity,high dimension and low rank,these characteristics bring new opportunities and challenges to statistical regression,and have attracted wide attention from experts and scholars in the fields of statistics,information science and biomedical science.This paper mainly discusses matrix re-gression for high dimensional constrained matrix regression model,by referring to a large number of literatures,it is found that most literatures transform them into convex optimization problems with matrix as decision variable for solving.The ideas of these findings can be divided into the following two categories:one is to transform it into a nuclear norm canonical model,which satisfys the penalty of nuclear norm,can solve the problem of high dimensional matrix regression with low rank constraint.The other is to transform it into a block regular model,which satisfies the penalty of ll/lq nor-m,can solve the problem of high dimensional matrix regression with block constraint.According to these two classic ideas,this paper presents the block and low-rank ma-trix regression model can solve the problem of high dimensional matrix regression with low rank constraint and block constraint,which satisfies nuclear norm penalty and l1/l2 norm penalty.In the large scale and fast optimization algorithm of the design optimiza-tion model,the multiplier alternating direction method is widely concerned.Therefore,a linear multiplier alternating direction algorithm is designed for the block low rank matrix regression model,we also shows that this algorithm has convergence,numerical results are reported to demonstrate the efficiency of our algorithm.