Iterated Discriminate Method

Content: On the problem of multi-groups discrimination, the correct rates of back substitution of existing discriminate methods may be good for some data, yet it is not the case for another data. Furthermore we can't evaluate the results of the discriminations. This article puts forward an improved new discriminate method based on the existing discriminate methods-Iterated Discriminate Method. Iterated discriminate method has two implications: one is the process of iteration of choosing groups, the other is adding the step discrimination during the process of iteration of choosing groups. Its essential idea is: ①,From G1,G2,…,Gk choose a group Gα1,it can be satisfied that Gα1 can distinguish each sample to a greatest extend, i.e., using the existing discriminate methods (choosing index and not-choosing index) to judge each sample whether in Gα1 or not in Gα1 so as to maximize the correct rates of back substitution. We can establish such a model in the form of:δ1(x)=0 x∈Gα1 1 x∈Gα1 (1) ②,Eliminating each sample in group Gα1,from the remained k-1 groups G1,G2,…,Gα1,Gα1+1,,Gk,,Gk=G-Gα1,(n-nα1 samples),searching another group Gα2 again to separate each sample to the highest extend,i.e., using the existing discriminate methods (choosing index and not-choosing index) to judge each sample whether in Gα2 or not in Gα2 so as to maximize the correct rates of back substitution. We can establish another model in the form of:δ2(x)=0 x∈(G-Gα1) Gα2 1 x∈Gα2 (2) Go ahead in the same way until there are two groups left. Then we can construct k-1 discriminate models:δi(x)=0 x∈(G-Gα1- … -Gαi-1) Gαi (with i=1,2, ,k-1) (3) 1 x∈Gαi (with i=1,2,...,k-1)For any sample x, put it into model(1).Ifδ1 (x)=1,then we can conclude that x∈Gα1,else put it into model(2) continually; Ifδ2 (x)=1,then we can reach that x∈Gα2,else continue in the same way until someδi (x)=1;then we can judge x∈Gαi 。For some data having multi-groups we can use general discriminate methods (In this article taking Fisher,Bayes,Gravitation these three methods for example) and iterated discriminate methods. The results show that iterated discriminate method is better than general discriminate methods. We need a standard for evaluating some data having multi-groups the results of classification. This paper gives the definition of "Loss Matrix of Groups Distance". Using this definition we can illustrate the loss of misclassification in multi-groups quantitatively and more practically.