Radial Basis Function Neural Network

This is a radial basis function neural network, which employs RBF network learning algorithms to approximate a two-dimensional function and utilizes the LMS algorithm for weight adjustment. The network architecture is based on the concept of radial basis functions, enabling nonlinear mapping of input data to enhance the model's expressive capability. In this implementation, the network typically consists of three layers: an input layer, a hidden layer with Gaussian activation functions, and a linear output layer. The learning algorithm adjusts network weights to better approximate the target function. Specifically, the LMS (Least Mean Squares) algorithm calculates network errors and updates weights based on error magnitude. The weight update formula follows: Δw = η * (target - output) * φ(x), where η represents the learning rate and φ(x) denotes the radial basis function output. Key implementation aspects include: - Gaussian function calculation: φ(x) = exp(-||x - c||² / (2σ²)) for hidden neurons - Center selection using k-means clustering or random sampling - Width parameter (σ) determination through neighbor distance analysis - Output computation: y = Σ w_i * φ_i(x) + bias This approach effectively improves network accuracy and performance, making radial basis function neural networks a powerful tool for two-dimensional function approximation and weight adjustment problems. The method demonstrates particular strength in handling nonlinear relationships with fast convergence properties.