MATLAB Code Implementation of RBF Neural Networks

RBF (Radial Basis Function) neural networks are efficient feedforward neural networks particularly adept at function approximation and pattern recognition tasks. Their core concept involves transforming input spaces nonlinearly through radial basis functions (such as Gaussian functions), then achieving complex mappings through linear combinations.

Implementing RBF neural networks in MATLAB typically involves the following key steps:

Network Initialization Determine the number of hidden layer nodes (i.e., the number of radial basis function centers), typically using K-means clustering algorithm to automatically select center points from training data. Set the width parameter (σ) for radial basis functions, which affects the smoothness of the function. In MATLAB implementation, this can be achieved using the kmeans function for center selection and calculating σ based on inter-center distances.

Hidden Layer Computation Each hidden layer node corresponds to a radial basis function, calculating the Euclidean distance between input data and center points, then converting it to nonlinear responses through Gaussian functions. This step maps the original input space to a high-dimensional feature space. Code implementation typically involves vectorized distance calculations using pdist2 function and applying exp() operations for Gaussian transformations.

Output Layer Weight Training The connection from hidden layer to output layer is linear, where weights can be directly solved using pseudo-inverse method or iteratively optimized through gradient descent. The pseudo-inverse method (using pinv function) is computationally efficient for small-scale data, while gradient descent (implemented through custom optimization loops) is more suitable for online learning scenarios. The weight calculation formula is W = pinv(H)*T, where H is the hidden layer output matrix and T is the target output.

Prediction and Evaluation For new input data, first compute radial basis function responses through the hidden layer, then combine linearly with trained weights to obtain output. Network performance can be evaluated using metrics like Mean Squared Error (MSE). Implementation involves using the same hidden layer computation followed by matrix multiplication W*H for final predictions.

MATLAB implementation of RBF neural networks can utilize built-in functions (like newrb or newrbe), but custom implementations offer more flexible parameter control. Their advantages include fast training speed and strong approximation capabilities, though attention must be paid to center point selection and overfitting issues. Practical applications commonly include time series prediction, control systems, and nonlinear classification scenarios. Custom implementations allow for tuning spread parameters and regularization techniques to prevent overfitting.