Robust recursive least squares learning algorithm for principal component analysis.

Area of Science:

• Machine Learning
• Signal Processing
• Computational Neuroscience

Background:

• Principal Component Analysis (PCA) is crucial for dimensionality reduction.
• Existing sequential PCA algorithms can suffer from error accumulation.
• Adaptive learning algorithms are needed for efficient PCA.

Purpose of the Study:

• Develop a robust and accurate learning algorithm for PCA.
• Improve convergence speed and component extraction.
• Address limitations of sequential PCA.

Main Methods:

• Least-square minimization for PCA.
• Adaptive adjustment of dual learning rate parameters.
• Analysis of unnormalized and normalized weight vector updates (leaky Hebb's rule).

Main Results:

• The algorithm achieves fast convergence and high accuracy in extracting all principal components.
• Demonstrated robustness against error accumulation in sequential PCA.
• Established a relationship between Oja's rule and least squares learning.

Conclusions:

• The proposed algorithm is effective for PCA and tracking time-varying directions-of-arrival.
• Unnormalized weight vectors fully represent PCA information.
• The method offers an improvement over existing PCA techniques.