Range-based ICA using a nonsmooth quasi-newton optimizer for electroencephalographic source localization in focal...

Area of Science:

• Signal Processing
• Computational Neuroscience
• Optimization Theory

Background:

• Independent Component Analysis (ICA) seeks to decompose multivariate signals into independent components without prior knowledge of the mixing process.
• Hartley-entropy-based ICA contrasts offer advantages, including guaranteed absence of local optima, but their non-differentiability limits optimization methods.
• Existing optimization techniques for ICA are often restricted to derivative-free methods due to contrast function properties.

Purpose of the Study:

• To develop a novel optimization scheme for a differentiable ICA contrast function.
• To address the limitations of derivative-free methods in ICA by employing a Riemannian quasi-Newton approach.
• To enhance the efficiency and reliability of ICA, particularly for electroencephalographic (EEG) data analysis.

Main Methods:

• A Riemannian quasi-Newton scheme is proposed, utilizing an explicit gradient expression for optimizing a differentiable ICA contrast function.
• The method incorporates an inexact line search with the weak Wolfe condition and a specialized terminating criterion for partly smooth functions, adapted for manifold settings.
• The approach is validated using diverse image datasets and EEG data from epileptic subjects.

Main Results:

• The proposed Riemannian quasi-Newton method demonstrates computational savings compared to existing techniques.
• The approach achieves reliable source localization in electroencephalographic (EEG) data, crucial for neurological studies.
• Experimental results confirm the efficacy and robustness of the new optimization strategy for ICA.

Conclusions:

• The developed Riemannian quasi-Newton scheme effectively optimizes differentiable ICA contrast functions, overcoming previous limitations.
• This method offers a computationally efficient and reliable alternative for signal separation and source localization tasks.
• The approach shows significant promise for applications in image processing and biomedical signal analysis, especially EEG.