Research On Discriminant Analysis Method Of Binary Classification Based On Risk Function

LDA(linear discrimination)and LR(logistic regression)are the two most widely used methods in dichotomy discrimination.Suppose the random variable x comes from a dichotomous mixed population,The two categories are respectively marked as y=land y=0,and the prior probability from the two categories is ?1,?0,?1+?0=1;we're going to categorize it according to the values of x.Eguchi s.&Copas j.(2002)put forward a risk function,which is composed of two penalty functions of U(s),V(s).Their independent variables is linear discriminating functionss.This penalty function should have two characteristics:when y=0(Y=1),the value of the penalty function will increase with the increase;When y=1(y=0),it will decrease with increasing.In this paper,based on the logarithmic dominance ratio in the N-P lemma,the logarithmic dominance ratio function in the linear form of LDA and LR is obtained in the case that the whole classification of the dichotomous classification is subject to a normal or exponential distribution.By minimizing the risk function,the optimal threshold of the linear dominance ratio function is determined,and a new criterion is established.It is proved that when the penalty function takes a special form,it is completely equivalent to the classical linear discriminant method and the classical Logistic regression discriminant method with the minimum error rate and the highest discriminant accuracy,indicating that this new classification method is more general.At the same time,the discriminant effect of LDA and LR under the same risk function is compared by numerical simulation and case analysis.The results show that LDA performs better when the sample data meet the assumptions of the same covariance and different mean vectors;otherwise,LR performs better.