MATLAB Implementation of RBF Neural Network Based on Least Squares Method

In this article, we provide a comprehensive guide on implementing RBF neural networks using MATLAB with a least squares optimization approach. Starting from fundamental definitions, we explain the working principle of RBF neural networks and demonstrate their MATLAB implementation through practical code examples. The implementation includes key functions such as radial basis function centers selection using k-means clustering, width parameter calculation using distance-based methods, and weight optimization through the pseudoinverse operation (pinv function in MATLAB) for efficient least squares solution. We analyze the algorithm's advantages in fast convergence and global approximation capabilities, while discussing limitations related to center selection sensitivity and computational complexity with large datasets. The article includes practical demonstrations of applying the algorithm to various datasets for prediction tasks, showcasing MATLAB's neural network toolbox functions and custom implementation approaches. Finally, we provide practical tips for parameter tuning, including guidelines for selecting appropriate spread constants and regularization techniques to prevent overfitting. This guide aims to deliver valuable insights for effectively understanding and applying least squares-based RBF neural networks in real-world scenarios using MATLAB's computational environment.