Building a Radial Basis Function Neural Network with Training Data and Plotting Input-Output Grid Diagrams

Radial Basis Function Neural Network (RBFNN) is a specialized type of feedforward neural network that employs radial basis functions as activation functions, characterized by simple structure and fast training capabilities. In engineering and scientific computing domains, RBFNNs are commonly applied to tasks such as function approximation, time series prediction, and pattern recognition. The process of constructing an RBF neural network typically involves several key steps: First, selecting appropriate radial basis functions (such as Gaussian functions), followed by determining the center positions of hidden layer neurons. Training data samples can be directly used as centers, or automated selection can be achieved through clustering algorithms like K-means. The core of network training lies in determining the connection weights between the hidden layer and output layer, which can be implemented using numerical optimization methods like least squares approximation. In MATLAB, this can be accomplished using functions such as newrbf() or custom implementations with radial basis calculations. After completing network training, plotting input-output grid diagrams serves as an effective method for visualizing network behavior. By uniformly sampling the input space and computing corresponding network output values, smooth surface plots can be generated. This visualization approach is particularly suitable for demonstrating how RBFNNs map input space to output space, providing significant insights into the network's approximation capability and generalization performance. Code implementation typically involves using meshgrid() for input sampling and surf()/mesh() functions for 3D visualization. For multi-dimensional input scenarios, projection methods or facet plotting techniques can be employed to display high-dimensional mapping relationships. The resolution of grid plots depends on sampling density, requiring a balance between computational cost and visualization quality. Such visualizations not only assist in debugging network parameters but also intuitively display the distribution of training data within the network. Advanced implementations may include dimensionality reduction techniques like PCA for high-dimensional data visualization.