The RBF Neural Network: A Three-Layer Feedforward Architecture with a Single Hidden Layer

The RBF (Radial Basis Function) neural network is a three-layer feedforward architecture comprising an input layer, a hidden layer, and an output layer. This code is designed to construct and train an RBF neural network model. As a widely used artificial neural network model, RBF networks have extensive applications in pattern recognition, function approximation, classification, and other domains. The network structure consists of three core layers, with the hidden layer serving as the computational heart—processing input data through a series of radial basis function calculations to enable learning. The primary objective of this code is to train the RBF neural network using provided training data, aiming to achieve accurate predictions for unseen data. During the training process, common optimization algorithms such as gradient descent or genetic algorithms are employed to iteratively adjust network weights and biases. This optimization minimizes the discrepancy between the network's output and the desired target values. Key implementation details include: radial basis function selection (e.g., Gaussian functions) for hidden layer activation, center initialization strategies for basis functions, and weight update mechanisms between hidden and output layers. Through iterative training cycles, the network's performance and accuracy are progressively enhanced, making it more effective in practical applications. The code structure typically involves data preprocessing, hidden layer configuration with radial basis functions, linear output layer computation, and a training loop that incorporates loss calculation and parameter updates using the chosen optimization algorithm.