MATLAB Source Code for RBF Neural Network Prediction Model

RBF (Radial Basis Function) neural network is a neural network model based on local approximation principles, commonly used for regression prediction and pattern recognition tasks. Its core concept involves mapping input data to high-dimensional space through nonlinear transformations of radial basis functions, enabling modeling of complex nonlinear relationships.

Key implementation steps for building an RBF neural network prediction model in MATLAB include:

Data Preprocessing Input data typically requires normalization (such as Min-Max scaling or Z-Score standardization) to mitigate numerical discrepancies caused by different feature scales. The dataset should be divided into training, validation, and test sets using MATLAB's `cvpartition` function or manual splitting techniques.

Network Initialization The RBF network structure consists of an input layer, hidden layer (radial basis layer), and output layer. Determining the number of hidden layer nodes (i.e., the quantity of radial basis functions) is crucial, with common initialization methods including random selection or K-means cluster centers. In MATLAB, this can be implemented using `kmeans` function for center initialization.

Radial Basis Function Selection Gaussian function is the most commonly used radial basis function, where the width parameter (σ) influences the function's local response range. Optimal parameters can be determined through cross-validation or heuristic rules, implemented via MATLAB's optimization toolbox or custom grid search algorithms.

Weight Calculation The weights from hidden layer to output layer are typically solved directly using least squares method, which contributes to RBF network's training efficiency. This can be implemented using MATLAB's backslash operator (`\`) or the `pinv` function for pseudoinverse calculation.

Model Evaluation Prediction performance is evaluated using metrics such as Mean Squared Error (MSE) or Coefficient of Determination (R²), with model optimization achieved by adjusting hidden layer nodes or basis function parameters. MATLAB's `mse` function and custom R-squared calculation functions can be employed for evaluation.

Extension Approaches: For dynamic system prediction, input features can be constructed by combining time series sliding windows using MATLAB's `buffer` function or custom lag operations. For high-dimensional data, PCA dimensionality reduction is recommended to reduce computational complexity, implementable via MATLAB's `pca` function. While MATLAB provides quick RBF network implementation through `newrb` or `fitnet` functions, custom implementation offers greater flexibility in parameter control and algorithm modification.