Improving the ability of function approximation of neural network using patulous cross section method

Neural network (NN) can approximate a random function in random precision. But overtraining is a defect that is difficult to overcome when plentiful specimens have not been provided. In this paper, a patulous cross section method (PCSM) is presented. This method partitions the multi-dimension input (or output) specimen space of NN into many curve surfaces in lower space, and then partitions every this curve surface into many curves. By curve fitting, many new "additional specimens" can be obtained. The precision of curve fitting is so high that the "additional specimens" can be used as the training specimens of NN. The applying example in the end of this paper shows that, with these "additional specimen", overtraining of NN can be overcome.