Sensitivity Analysis On Rational Spline Weight Function Neural Network With Cubic Numerator And Quadratic Denominatorand And Its Application

The sensitivity is an important indicator to the neural network. It is the disturbance which measures the networks’ performance caused by the disturbance of inputs of the network or other parameters. Analyzing the change of sensitivity theoretically is helpful to get acquaintance with the ability of anti-interference and enhance the ability of the network.The spline weight function neural network which is proposed in the book "The New Theories and Mmethods on Neural Network" is a totally new kind of neural network. This paper analyzes the sensitivity of neural netwok of rational spline weight function with cubic numerator and quadratic denominator on the basic of topology structure and training method of spline weight function combined with the Peano kernel theorem, definition of the statistical sensitivity. Firstly the model error and the approximation error of noise is analyzed and the computational formula of sensitivity is deduced. The corresponding experiment is based on the MATLAB simulation.The theoretical analysis and the simulations show that the neural netwok of rational spline weight function with cubic numerator and quadratic denominator has fast training speed, better anti-interference and the error is small when the input disturbance is small.This paper comes to the conclusions that the neural network of rational spline weight function with cubic numerator and quadratic denominator has the advantages of simple topology structure, fast training speed, small error and the ability of anti-interference. Besides, we can predict the deviation between actual outputs and theoretical ouputs according to the sensitivity.The application part of this paper is the recognition of heart disease. The 13 kinds of data associated with heart disease after normalization such as age, gender, and heart rate are set as inputs and we can detect whether people have heart disease according to the outputs. The neural network of rational spline weight function with cubic numerator and quadratic denominator has faster training speed and better recognition than BP neural network. So it has a broad prospect.