Nonsmooth ICA contrast minimization using a Riemannian Nelder-Mead method

Area of Science:

• Signal Processing
• Optimization
• Machine Learning

Background:

• Source separation is crucial for isolating individual signals from mixed data.
• Nondifferentiable contrast functions offer discriminative properties but pose optimization challenges.
• Derivative-free optimization is needed for such functions.

Purpose of the Study:

• To design and apply a Riemannian Nelder-Mead algorithm for source separation.
• To minimize a Hartley-entropy-based contrast function for reliable source estimation.
• To address the challenges of optimizing nondifferentiable functions in source separation.

Main Methods:

• Developed a Riemannian Nelder-Mead algorithm tailored for the oblique manifold constraint set.
• Utilized a Hartley-entropy-based contrast function, known for its discriminacy.
• Employed a derivative-free optimization approach to handle the nondifferentiable function.

Main Results:

• The proposed Riemannian Nelder-Mead algorithm successfully minimized the contrast function.
• Empirical studies demonstrated reliable source separation from quasi-correlated synthetic signals.
• Digital image source separation tasks also showed favorable results compared to other methods.

Conclusions:

• The Riemannian Nelder-Mead algorithm is effective for source separation using nondifferentiable contrast functions.
• Derivative-free optimization on manifolds is a viable approach for complex signal processing tasks.
• The method shows promise for applications requiring robust source estimation.