A spectral clustering approach to underdetermined postnonlinear blind source separation of sparse sources

Area of Science:

• Signal Processing
• Machine Learning
• Information Theory

Background:

• The underdetermined postnonlinear blind source separation (PNL BSS) problem, where the number of observed mixtures is less than the number of sources, remains a significant challenge, particularly when sources are sparse.
• Existing methods often address either linear underdetermined BSS or nonlinear BSS with an equal number of mixtures and sources, leaving a gap for the nonlinear underdetermined case.

Discussion:

• This work proposes a clustering-based strategy to tackle the underdetermined PNL BSS problem with sparse sources.
• The core idea is to invert the nonlinearities present in the mixtures, effectively transforming the problem into a more manageable linear underdetermined BSS scenario.
• This transformation is achieved through spectral clustering to group mixture samples and multilayer perceptrons (MLPs) to estimate inverse nonlinearities.

Key Insights:

• A novel spectral clustering technique is employed to partition mixture samples, associating them with their respective original sources.
• Multilayer perceptrons (MLPs) are trained to learn and estimate the inverse nonlinear transformations for each identified source cluster.
• Successful inversion of nonlinearities reduces the complex PNL BSS problem to a standard linear underdetermined BSS problem, solvable by existing algorithms.

Outlook:

• This approach offers a promising solution for underdetermined PNL BSS in scenarios with sparse sources.
• Further research could explore the application of this method to real-world signal separation tasks.
• Investigating the scalability and robustness of the MLP-based nonlinearity inversion could enhance its practical utility.