Construction And Analysis Of Unbiased Sparse Human Brain Hyper-Network Based On Predefined Group

Due to the development and maturity of Resting Functional Magnetic Resonance Imaging(R-f MRI)technology,it has now been applied to predict depression and other brain diseases at large.The hyper-network is widely used because it can fully reflect the interaction between various brain regions.The hyper-network construction methods that exist today are practically in the light of the sparse representation idea.The sparse representation method that traditionally according to LASSO model lacks the ability to explain the group effect between brain regions.Therefore,a group-based hyper-network construction method is proposed,but there are still limitations: on the one hand,they are mostly based on automatic grouping,ignoring the complex a priori group structure in the human brain;on the other hand,they can only make a single-level selection and ignore the complex hierarchical relationship in the human brain;furthermore,owing to the too strong compression effect of the penalty function on the coefficients,and it leads to a biased estimation of the regression coefficients of the target variables in the model,so that while the noise variables are compressed,the target variables are also compressed to a certain extent.Thence,this paper takes questions above into consideration,and on the basis of the group effect problem,proposes three hyper-network construction methods based on predefined grouping unbiased sparse models to improve the original method: the composite Minimax Concave Penalty(MCP)method,the group MCP method and the group Smoothly Clipped Absolute Deviation(SCAD)method.The first method can not only select variables between groups,but also select important variables within the group,called bi-level selection;the latter two methods do not have bi-level selection capabilities,and can only select variables at the group level.However,the composite MCP and the group MCP methods are both based on the unbiased sparse model of the Minimax Concave Penalty(MCP),while the group SCAD model utilizes the SCAD penalty on the group level to achieve group selection.The experimental results show that structures of hyper-networks constructed by the three methods are different.The hyper-network structure constructed by the group MCP method and the group SCAD method is similar,but the two are quite different from the hyper-network structure based on the composite MCP method.The results of classification performance reveal that the composite MCP method has better classification performance than the other two methods.Besides,among the hyper-network construction methods based on predefined groupings,the composite MCP method has a better ability to explain grouping effect.The brain functional hyper-network constructed by the method proposed in this article can better express the structural differences between depression patients and normal controls,and has eventful theoretical and clinical worth.The main innovations of this paper are as follows:Firstly,the construction of brain functional hyper-network is on the basis of predefined groups.The automatic group effect model only implements group selection for variables with strong correlation,and does not take into account the group structure naturally formed in the human brain.The predefined grouping model can select groups of arbitrary variables,and also takes into account the relevant variables in the human brain.The composite MCP,group MCP and group SCAD methods all define the number of groups artificially,the clustering algorithm is applied to divide variables that are relevant into specific groups,and the group can be selected for any variable by repeating it many times.Secondly,propose a brain function connection modeling method based on unbiased sparse model.The composite MCP,group MCP and group SCAD methods are all based on the unbiased sparse model for hyper-network construction.The LASSO model is a traditional method of constructing brain networks,but this method is a biased estimation,which is mainly reflected in the estimation of the regression coefficients of the target variable in the process of solving the sparse linear model.The reason why LASSO produces biased estimates is that the degree of compression of the regression coefficients of the noise variable and the target variable is the same.Therefore,for the disadvantage of biased estimation of LASSO,an unbiased sparse model is introduced.Compared with the LASSO method,the unbiased sparse model used by the three hyper-network construction methods shows a gradual decrease in the degree of compression of the regression coefficients of the target variables,and it is even possible to completely eliminate the compression of the regression coefficients of the target variables..Thirdly,the bi-level selection of variables.On the basis of the group structure,bi-level selection is introduced,which refers to the ability to select variables at the group level and to select important variables within the group,therefore,the variable selection is more strict,but it can best reflect the complexity hierarchy of the human brain.The results show that the composite MCP method with bi-level selection has the best classification performance.The three brain functional hyper-network construction methods proposed in this paper can effectively solve the problem of biased estimation for LASSO and various sparse representation models based on LASSO,and better express the complex hierarchical relationships in the human brain structure.The experimental results show that the brain functional hyper-network construction methods of unbiased sparse model based on predefined grouping have better classification performance and higher classification weight.The work of this paper has been supported by the National Natural Science Foundation of China(61472270,61672374,61741212,61876124,61976150),Shanxi Provincial Key R&D Program Project(201803D31043),Shanxi Provincial Department of Science and Technology Applied Basic Research Project Youth General Project(201801D121135,201803D31043),Shanxi Province Supported by the Provincial Department of Education’s Science and Technology Innovation Research Project(2016139)in Higher Education Institutions and the Ministry of Education’s Next Generation Internet Technology Innovation Project(NGII20170712).The focus of this article is that the hyper-network construction method of unbiased sparse model has important theoretical significance and clinical value for the classification of patients with depression.