Prediction Using Radial Basis Function Neural Networks

Radial Basis Function Neural Networks (RBFNN) are widely used for function approximation, classification, and prediction tasks due to their simple architecture and efficient training process. The core concept involves mapping input data to a high-dimensional space through nonlinear transformations using radial basis functions, enabling the solution of complex nonlinear problems.

In predictive modeling, RBFNN typically consists of three layers: input layer, hidden layer, and output layer. The input layer receives raw data, the hidden layer calculates distances between inputs and center points using radial basis functions (e.g., Gaussian functions), while the output layer performs linear weighted combinations to generate predictions. The MATLAB implementation utilizes functions like `newrb` for exact interpolation or `fitnet` with radial basis activation functions for flexible network configuration.

MATLAB provides convenient toolbox functions (such as `newrb` or `fitnet`) for RBFNN implementation. Key steps include: Data Preprocessing: Normalize input and output data using functions like `zscore` or `mapminmax` to prevent numerical scale discrepancies from affecting training. Hidden Layer Parameter Determination: Select radial basis functions (e.g., Gaussian kernel) and set center points (initialized via K-means clustering using `kmeans` function or random sampling). Network Training: Employ supervised learning algorithms (like gradient descent) through `train` function to optimize weights and minimize prediction errors. Validation and Testing: Evaluate generalization capability through cross-validation techniques (`crossval`) to prevent overfitting.

RBFNN's advantage lies in its strong local approximation capability, making it suitable for small-to-medium-sized datasets. However, it may face the "curse of dimensionality" with high-dimensional data. Improvement approaches include incorporating regularization techniques (`regularization` parameter in training functions) or optimizing center point selection strategies through advanced clustering algorithms.