Studying Functional Data Classification Based On Conformal Prediction

Functional data classification is an important area of research in functional data analysis,which has been widely used in life sciences,medicine and economics.Most of the common functional data classification methods give only one classification result,the shortcoming is that they cannot quantify the uncertainty of the result.Conformal prediction is a common method to quantify uncertainty of prediction by constructing prediction intervals(for regression problems)or sets(for classification problems).In this thesis,we propose a new functional data classification algorithm based on the conformal prediction method.This algorithm can construct a prediction set that satisfies a given coverage to quantify the uncertainty of the classification result,and only requires the data to satisfy the exchangeability.First,we construct functional prediction bands that describe the range,size and shape of a set of curves by two methods.Then,a non-conformity score function is defined to measure the distance between the curves and the prediction bands,and two methods are designed to calculate the weight matrix.Finally,this thesis classifies the functional data according to the Mondrian inductive conformal prediction method.In the simulation study and real data analysis,the proposed algorithm can guarantee the coverage of each category at a given confidence level and performs better in terms of ambiguity(average size of the prediction set).