BP-Fisher Discriminant Analysis

Nonlinear discriminant analysis is one of the important branch subjects of pattern recognition. With social developing, nonlinear discriminant analysis is proposed for higher requirements. Therefore, to study the nonlinear discrimination has very important theoretical and practical significance. Traditional nonlinear discriminant analysis methods include: neural network and kernel method. The performance of the neural network is often influenced by the over fitting, the fitting and generalization performance rely heavily on network structure and parameters. The kernel method use kernel function to map the input data into a high dimensional feature space, and making linear classification for data in the feature space. However, kernel function has very important influence on the classification accuracy of kernel method and how to construct the kernel function for the actual problem is always a difficult problem in the field of kernel methods. In fact, the kernel method use experience function as a mapping function, this lack of flexibility.To solve the above problems, a new nonlinear discriminant analysis method is proposed,the research contents are as follows:(1) BP neural network, radial basis neural network,kernel method is further studied. On this basis, Schmidt orthogonal basis transformation method is proposed to obtain the output layer weights of RBF neural network.(2) Inspired by neural network and kernel method, a new nonlinear discriminant analysis method is proposed which named after BP-Fisher discriminant analysis method(BPFDA). In this method, BP neural network is used to construct the mapping function which maps input data into another in lower dimensional space, and object function is constructed by introducing Fisher criterion.So that the problem of discriminant analysis is converted into the optimization problem, and then using the differential evolution algorithm(DE) to solve it. The numerical experiments show that BPFDA has higher classification accuracy than other method.(3) The between class scatter matrix in BPFDA method was improved and BP-Fisher discriminant analysis based on the improvement between class scatter matrix method(NBPFDA) was proposed.The numerical experiments show that NBPFDA has better performance than the BPFDA when the number of hidden layer nodes is small. This provides new thoughts and new methods for nonlinear discriminant analysis.