cICA Implementation: Constrained Independent Component Analysis Algorithm

The cICA (constrained Independent Component Analysis) code provides a practical implementation of the constrained ICA algorithm, designed to separate multivariate signals into independent, non-Gaussian components. The algorithm incorporates specific constraints to ensure the extracted components maintain relevance to the target application. Key implementation steps include: - Data preprocessing: Centering and whitening operations to standardize input data - Constraint specification: Defining application-specific constraints through penalty terms or reference signals - Optimization process: Utilizing gradient-based methods (like natural gradient) to maximize non-Gaussianity while satisfying constraints - Objective function: Combining negentropy approximation with constraint terms using Lagrange multipliers The algorithm employs contrast functions (such as kurtosis or negentropy) to measure non-Gaussianity, with optimization typically handled through fixed-point iteration schemes. Performance evaluation metrics include: - Non-Gaussianity assessment using kurtosis or negentropy measurements - Separation accuracy via signal-to-interference ratio (SIR) or correlation coefficients - Constraint satisfaction verification through similarity measures The code structure typically involves modular functions for preprocessing, constraint handling, optimization loops, and result validation. This implementation serves as a powerful tool for signal processing applications across multiple domains including neuroscience (EEG/MEG analysis), financial data processing, and speech signal separation.