The Complexity Research On Neural Network With Quadratic Denominator Cubic Rational Spline Function Weight And Its Application

One problem can be sloved by different algorithms and the quality of algorithm will affect the efficiency of the program. Algorithm analysis aims to select the appropriate algorithm and improve algorithm, the quality of the algorithm is directly reflected in the complexity of the algorithm. This article aims to analyze the complexity and the application of the first type of rational spline weight function neural network which the numerator of the spline is a cubic polynomial and the denominator of the spline is a quadratic polynomial, denoted by 3/2 rational splines.Using 3/2 rational spline function as the weight function of neural network, combing the theory of spline weight function neural network, Hermite interpolation method and the properties of rational spline function, we establish linear equations and construct the 3/2 rational spline weight function neural network. Combing Peano Kernel theorem, Matrix LU method, linear equations solving method and algorithms complexity expression, we get the complexity of first type of 3/2 rational spline function neural network. Finally, we use MATLAB to simulate.We get the complexity formula of first type of 3/2 rational spline function neural network through theoretical analysis. The formula shows the algorithm complexity has linear relationship with the number of samples, the dimensions of input and output. The complexity expression is T ?O?mnN?. In the formla, m expresses input dimension, n expresses output dimension and N expresses the number of samples.The article confirms that the theoretical complexity of first type of 3/2 rational spline weight function neural network is correct through MATLAB simulations. When two variables of input dimensions, output dimensions and the number of sample are fixed, the time consumed of simulation has linear growth with the remaining variable. So we indicated this class of neural network has low time complexity and fast training speed.This article studys the application of network traffic classification based on 3/2 rational spline weight function neural network. This paper select appropriate feature items, build network traffic classification model for the first type of 3/2 rational spline function neural network. After data preprocessing, the artical makes MATLAB simulations and the experimental results show that the first type of 3/2 rational spline weight function neural network can apply in network traffic classification successfully and it has high accuracy.