Research On Adaptive Supervised Function Principal Component Regression Model And Its Medical Applicatio

Alzheimer’s disease is a chronic progressive neurodegenerative disease with an irreversible pathological process;therefore,early prediction of Alzheimer’s disease using imaging and biomarker data is of great clinical value.In this paper,we model Alzheimer’s disease-related data based on the theory of functional data analysis,and investigate how to simultaneously implement the introduction of nonlinear supervised information and adaptive transformation of variables in functional principal component regression models.The main content of this paper is divided into three parts as follows:In the first part,a new nonlinear supervised functional principal component regression model(SFPCA-R)is proposed.From the perspective of data transformation of scalar-type response variables,the transformation function is expanded using a B spline basis,improved in the framework of supervisory function principal component analysis,and the supervisory function principal components and transformation function coefficient vectors are estimated by iterative methods.After that,a comparison between Monte Carlo simulation and other supervised learning models reveals that the SFPCA-R model has a certain improvement effect on the prediction accuracy and outperforms the competing models when the response variable has a nonlinear relationship with the predictor variable.In the second part,a nonlinear supervised functional principal component regression model(SFPCA-P)that can perform both classification and regression prediction is proposed.From the perspective of data transformation of functional predictor variables,the transformation function is expanded using a B spline basis with monotonicity constraint,and the data transformation and supervised learning of functional principal components with high predictive power are achieved simultaneously.Compared with the SFPCA-R model,the SFPCA-P model has a better estimation of the transformation function,but the variance is larger and the model is not as robust as the SFPCA-R model.After that,numerical simulations using Monte Carlo methods are performed for the regression task and the classification task respectively,and it is demonstrated that their classification accuracy is better than the comparison methods in different transformation scenarios.In the third part,the SFPCA-R model was used for the regression prediction of missing indicators in Alzheimer’s disease,and the SFPCA-P model was applied to the classification discrimination of Alzheimer’s disease early detection,and the prediction effect was evaluated.,proving the validity of the model.