FastICA: The Most Classical Fixed-Point Algorithm in Blind Source Separation

FastICA stands as one of the most classical fixed-point algorithms in blind source separation, renowned for its concise implementation and high computational efficiency, making it particularly suitable for beginners entering the field. This algorithm is grounded in Independent Component Analysis (ICA) theory, designed to recover original independent source signals from mixed observations. The algorithm's core concept involves finding a linear transformation that maximizes statistical independence among output signal components. FastICA employs fixed-point iteration to optimize the objective function, achieving significantly faster convergence compared to traditional ICA algorithms. Key implementation steps include: 1. Centering and whitening preprocessing of observed data to remove correlations and standardize variances 2. Utilizing nonlinear functions (typically tanh or cubic functions) to approximate the independence of source signals through negentropy maximization 3. Implementing iterative updates using Newton's method approximations for stable convergence FastICA's advantages lie in its straightforward implementation, high computational efficiency, and minimal parameter tuning requirements. The algorithm finds extensive applications in speech signal separation, biomedical signal processing, financial data analysis, and various other domains, establishing itself as a primary choice for learning blind source separation techniques. Code implementations typically feature modular structure with separate functions for preprocessing, independence optimization, and component extraction.