A Unifying Objective Function of Independent Component Analysis for Ordering Sources by Non-Gaussianity

Area of Science:

• Signal Processing
• Statistical Learning
• Machine Learning

Background:

• Independent Component Analysis (ICA) is crucial for blind source separation.
• Traditional ICA methods maximize non-Gaussianity, often treating super- and sub-Gaussian sources separately.
• Existing methods face challenges with permutation ambiguity and determining the number of sources.

Purpose of the Study:

• To propose a novel objective function that unifies super- and sub-Gaussian source separation.
• To develop an algorithm that can automatically determine the number of non-Gaussian sources.
• To address the permutation ambiguity problem in ICA.

Main Methods:

• Developed the adaptive ICA function (AIF) by applying Gaussian approximation in a second-order polynomial feature space.
• AIF unifies non-Gaussianity using weighted fourth-order statistics with adaptively estimated weights.
• Constructed the ordering ICA algorithm by extending Fast ICA to leverage AIF's advantages.

Main Results:

• The proposed AIF successfully unifies different types of non-Gaussianity.
• The ordering ICA algorithm can extract sources sequentially, resolving permutation ambiguity.
• The Akaike Information Criterion, integrated into ordering ICA, accurately estimates the number of non-Gaussian sources.
• Experimental results validate the effectiveness on both artificial and real datasets.

Conclusions:

• The adaptive ICA function (AIF) offers a unified approach to blind source separation.
• Ordering ICA effectively addresses permutation ambiguity and accurately estimates the number of non-Gaussian sources.
• This method holds promise for improved performance in various signal processing applications.