Wavelet Neural Network with BP Learning Algorithm

A wavelet neural network implemented using the Backpropagation (BP) learning algorithm. This network architecture employs frame wavelet functions as activation functions in the hidden layer, while the output layer utilizes Sigmoid activation functions. To enhance learning efficiency, the network incorporates an entropy error function as the loss function, which significantly accelerates convergence during training. This wavelet neural network demonstrates strong learning capabilities and excellent generalization performance in pattern recognition and function approximation tasks. From an implementation perspective, the hidden layer wavelet functions can be implemented through mother wavelet transformations with adjustable dilation and translation parameters. The BP algorithm optimizes these parameters along with network weights using gradient descent. The entropy error function, typically implemented as cross-entropy loss, provides steeper gradients for faster weight updates compared to traditional mean squared error. The Sigmoid output activation ensures output values remain in the [0,1] range, making it suitable for classification tasks.