Multiple Regression Coefficient Sub-modules'Recognition Based On Convex Biclustering

In recent years,the research on mining potential combinatorial control modules has been widely concerned and developed.This mainly benefits from the research of combinatorial control modules that can reveal the internal combinatorial regulation mechanism between features to a certain extent.Now the research on this aspect mainly focuses on the field of genomics,such as the study of the correlation between genes and genes,and correlation between protein and genes,which has great research value in understanding its own function.Considering that there are some limitations in the current application scenes,this paper takes"Product Design Innovation Factor Analysis"and"China's Transportation Science and Technology Input and Output Analysis"as an example,and excavates the potential correlation sub-modules in the coefficient matrix on the basis of the study of multiple regression problems,and then studies the similarity of its internal action mechanism.In this paper,a two-stage algorithm model is established to identify the correlation relationship between different feature groups,that is,using multiple-output sparse group lasso model to build coefficient control matrix in the first stage based on response variables,predictive variables and group information of predictive variables and using convex biclustering model to obtain"response variables-predictive variables”global optimal association sub-modules in the second stage based on the coefficient matrix.The numerical simulations show that the two-stage algorithm model can not only filter out important group variables and important intra-group variables with the help of multiple-output sparse group lasso model in the first stage,but also obtain the global optimal and stable association sub-modules of"response variables-predictive variables'”with the help of convex biclustering model in the second stage.The empirical applications show that the two-stage algorithm model can excavate the potential association sub-modules in the coefficient matrix,and reveal the similarity of the internal action mechanism of the response variables and predictive variables to a certain extent,and also reflect the strong practicability of the two-stage algorithm model proposed in this paper.