Discriminant Analysis Of High-Dimensional And Multi-Population Based On Features Annealed Independence Rules

This paper mainly studies the classification of high-dimensional data when covariance matrices are equal under multi-population normal distribution.The existing results show that the independent classification method is more e?ective than the linear discriminant method for the two categories of normal distribution problems.Fan points out in the literature that if all the features were used for classification,the independent classification rule would still be poor.To emphasize the ability of feature recognition,Fan proposed the principle of feature annealed independence rule.Based on Fan's theory,this paper proposes FAIR of multi-population,and selects the most statistically significant m features according to the component ANOVA between the K classes,and applies independent classifier on these m features.The selection of the best number of features is based on the upper bound of misclassification rate.Simulation analysis supports the theoretical results of this paper and convincingly illustrates the advantages of the new method.This paper will be introduced from the following parts: the first part introduces the background knowledge of this paper,the research status and development trend of discriminant analysis.The second part introduces the applied model and discriminant function.The third part is the core of this paper,which are two important theorems.The fourth part are the proof of two theorems.The simulation of the fifth part proves the correctness of the theoretical results.