MATLAB Implementation of Wavelet Neural Networks

Wavelet Neural Network (WNN) is a hybrid model that combines wavelet transform and artificial neural networks, featuring excellent capability for feature extraction and nonlinear approximation. The core concept involves using wavelet functions as activation functions for neurons, thereby enhancing the network's ability to capture time-frequency localized characteristics. In MATLAB, implementing a wavelet neural network typically involves the following key steps: Data Preprocessing: Input data requires normalization or standardization to ensure consistent feature scales for effective network training. For time series or signal data, wavelet decomposition may be necessary to extract multi-scale features. In code implementation, this can be achieved using functions like normalize for data scaling and wavedec for wavelet decomposition. Network Architecture Design: WNN typically consists of input layer, hidden layer, and output layer. The hidden layer neurons employ wavelet basis functions (such as Morlet, Mexican Hat) as activation functions. Network weights and scaling parameters require initialization adjustments based on specific tasks. The network structure can be defined using neural network toolbox functions like feedforwardnet with custom activation functions. Training Algorithm: Error Backpropagation (BP) algorithm or its improved versions (such as momentum BP algorithm) can be employed for training. During training, both the translation and scaling parameters of wavelet basis functions and network weights are optimized simultaneously to enhance the model's fitting capability. This can be implemented using train function with customized training parameters and optimization settings. Performance Evaluation: After training completion, the model's generalization performance must be validated using test datasets. Common evaluation metrics include Mean Squared Error (MSE) and correlation coefficients. For classification tasks, accuracy, recall rate, and other classification metrics should be monitored. MATLAB provides functions like perform for error calculation and confusionmat for classification evaluation. Wavelet neural networks have demonstrated successful applications in signal denoising, fault diagnosis, financial prediction, and other domains. Their advantage lies in the ability to adaptively extract local features from data while leveraging neural networks' nonlinear modeling capabilities, resulting in superior performance on complex datasets.