| What we study in this paper is the design of the output layer nodes on basis of the mechanism of feed-forward neural networks for solving multi-classification problem with r(r≥3).The common and conventional one-for-each approach is as follows:The output layer contains r output nodes,the number of which is equal to the number of the classes of the input samples.For an input sample of the i-th class(1≤i≤r),the ideal values of the output layer is 1 for the i-th output node,and 0 for all the other output nodes.We put forward in this paper another novel approach called binary approach,of which the ideal output for a certain class may contain two or more "1".Let2q-1<r≤2q with q≥2,for a classification problem with r,the binary approach correspond to a neural networks which contains q output nodes,and the ideal outputs for the r classes manner in a binary number.In this paper,we first simplify the three layers neural networks into two layers networks of hidden layer and output layer,according to the fact that the output of hidden layer is just decided by the number of hidden nodes directly not the input samples and that the output of hidden layer is decided by the output of hidden layer.Then we can the classification problem in another way,where we just classify the vertices of the regular cube in the Euclidean Space.We mainly consider the number of hidden nodes is four according to that the results of two and three hidden nodes is mature.We prove in this paper that if the classification problem can be solved by one-for-each approach,binary approach does equally good job for the same problem,but uses less output nodes,and binary approach can solve some classification problems that one-for-each approach cannot.So our approach is advisable:binary approach not only reduces the complexity of the neural networks,but also solves more classification problems. |
