Learning algorithm of wavelet network based on sampling theory

To avoid overfitting, the sampling theory is applied to training of wavelet networks. A new algorithm is proposed based on the limited band of wavelet networks, in which the input weights are decided by the sampling period or the frequency band of target function instead of sample errors. The wavelet networks trained by our new algorithm have global convergence, avoidance of local minimum and ability to approximate band-limited functions. Our new algorithm is also extended to learn from noisy data. The theorems prove that the wavelet network trained by our new algorithm is just an ideal low-pass filter, which removes the high-frequency noise in training data. In the simulation, we compare the performance of new algorithm with that of regularization technology. The results show that our algorithm is more robust to the variance of noise and removes high-frequency noise more effectively.