Prediction of noisy chaotic time series using an optimal radial basis function neural network

Area of Science:

• * Computational neuroscience
• * Time series analysis
• * Machine learning

Background:

• * Predicting chaotic time series is challenging, especially with noise.
• * Radial basis function (RBF) networks are used for nonlinear function approximation.
• * In noiseless conditions, RBF predictors require infinite hidden units for optimal generalization.

Purpose of the Study:

• * To develop an optimal prediction method for noisy chaotic time series using RBF networks.
• * To propose a novel technique for determining the optimal number of hidden units in RBF predictors.
• * To address the issue of overfitting in noisy data prediction.

Main Methods:

• * Application of radial basis function (RBF) networks for time series prediction.
• * Development of the cross-validated subspace method to estimate the optimum number of hidden units.
• * Utilizing subspace techniques to identify signal subspace dimension via eigenvectors.
• * Employing cross-validation to mitigate overfitting.

Main Results:

• * Demonstrated that optimal RBF predictors for noisy data require a finite number of hidden units.
• * Validated the effectiveness of the cross-validated subspace method on simulated and real-world data.
• * Showcased the method's ability to identify the correct number of hidden units for optimal prediction.

Conclusions:

• * The cross-validated subspace method is effective for determining RBF network structure in noisy chaotic time series prediction.
• * This approach balances model complexity and predictive accuracy, preventing overfitting.
• * The findings advance the field of chaotic time series analysis and RBF network optimization.