Comparison study of fast independent component analysis and constrained independent component analysis

Constrained Independent Component Analysis (cICA) was developed from Independent Component Analysis (ICA), and the concepts and principles of independent component analysis still apply to constrained independent component analysis. This paper introduces the mathematical basis, basic principles and algorithms of constrained independent component analysis. Firstly, the mathematical basis of cICA is introduced. It mainly includes the entropy and negative entropy of irrelevant and whitening, Statistical opposition and multivariate Gaussian density random variables. Then the mathematical model of Constrained FastICA, the identifiability and uncertainty of the model, the FastICA independence criterion, FastICA optimization and preprocessing, FastICA algorithm and simulation examples are introduced. Finally, the shortcomings of fast independent component analysis and the advantages of constrained independent component analysis are analyzed. According to the establishment and evaluation indicators of signals, the basic principles and corresponding algorithms of constrained independent component analysis are introduced. The characteristics of the corresponding simulation show that the algorithm is effective in extracting signal characteristics.