Research On Interpretability Classification Method Based On Imbalanced Functional Data

This thesis mainly studies the interpretable classification method of imbalanced functional data,which can be divided into three subproblems: variable selection,im-balanced data processing,and functional data classification.Firstly,this thesis uses the semi-parametric model called sparse interval sliced inverse regression(SISIR),which is extended from sliced inverse regression(SIR).In order to deal with the high-dimensional characteristics of functional data,SISIR uses ridge SIR model to reduce the dimension.Through the process of sparseness and interval fusion,this method can select effective feature intervals instead of discrete features,which improves the interpretability of the estimated coefficients in functional framework.In order to solve classification prob-lem of imbalanced functional data,this thesis deals with imbalanced functional data by ways of synthetic minority over sampling technique(SMOTE),which synthesizes ar-tificial data to balance samples.On the last,functional logistic regression is used to classify the functional data processed by SMOTE method.The convergence of the pa-rameters in the functional logistic regression model is proved while the binary functional logistic regression is extended to multivariate form.After the verification of the actual data set and compared with other common classification algorithms,the SSFLR method proposed by this thesis has won good effect and high accuracy in the classification of imbalanced functional data.