How many separable sources? Model selection in independent components analysis.

Area of Science:

• Data analysis
• Statistical modeling
• Signal processing

Background:

• Standard Independent Component Analysis (ICA) struggles with mixtures containing Gaussian components.
• ICA relies on higher-order statistics, which are ineffective for Gaussian sources.

Purpose of the Study:

• To introduce a novel mixed Independent Component Analysis/Principal Component Analysis (ICA/PCA) model.
• To address the challenge of separating mixtures with one or more Gaussian components.

Main Methods:

• Developed a mixed ICA/PCA model to accommodate Gaussian components.
• Utilized Principal Component Analysis (PCA) to characterize the inseparable Gaussian subspace.
• Employed information theory and cross-validation for model selection.

Main Results:

• The proposed mixed ICA/PCA model successfully integrates Gaussian components.
• Simulation studies indicated that Akaike Information Criterion (AIC) is unsuitable for model selection in this context.
• Cross-validation proved to be a viable, albeit computationally intensive, alternative for model selection.

Conclusions:

• Mixed ICA/PCA offers a robust method for analyzing data with Gaussian and non-Gaussian sources.
• The findings have implications for fields requiring authentic source separation.
• Highlights the limitations of AIC in specific statistical modeling scenarios.