2024/01/16 by Syamantak Kumar, Purnamrita Sarkar, Kumar, Syamantak +5
Chemistry · Computer Science · Engineering · #Blind Source Separation Techniques #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #Machine Learning (cs.LG) #Signal Processing (eess.SP) #Sparse and Compressive Sensing Techniques #Spectroscopy and Chemometric Analyses #Statistics Theory (math.ST) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2401.08468
openalex publication_date 2024/01/16 · openalex created_date 2024/01/18 · openalex updated_date 2026/07/28
Independent Component Analysis (ICA) was introduced in the 1980's as a model for Blind Source Separation (BSS), which refers to the process of recovering the sources underlying a mixture of signals, with little knowledge about the source signals or the mixing process. While there are many sophisticated algorithms for estimation, different methods have different shortcomings. In this paper, we develop a nonparametric score to adaptively pick the right algorithm for ICA with arbitrary Gaussian noise. The novelty of this score stems from the fact that it just assumes a finite second moment of the data and uses the characteristic function to evaluate the quality of the estimated mixing matrix without any knowledge of the parameters of the noise distribution. In addition, we propose some new contrast functions and algorithms that enjoy the same fast computability as existing algorithms like FASTICA and JADE but work in domains where the former may fail. While these also may have weaknesses, our proposed diagnostic, as shown by our simulations, can remedy them. Finally, we propose a theoretical framework to analyze the local and global convergence properties of our algorithms.