skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


This content will become publicly available on November 5, 2025

Title: Nonparametric Evaluation of Noisy ICA Solutions
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.  more » « less
Award ID(s):
2505865
PAR ID:
10631142
Author(s) / Creator(s):
; ; ;
Publisher / Repository:
https://doi.org/10.48550/arXiv.2401.08468
Date Published:
ISSN:
2401.08468
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. ; ; ; ; ; ; ; ; (, Technologies)
    null (Ed.)
    Monitoring of fetal electrocardiogram (fECG) would provide useful information about fetal wellbeing as well as any abnormal development during pregnancy. Recent advances in flexible electronics and wearable technologies have enabled compact devices to acquire personal physiological signals in the home setting, including those of expectant mothers. However, the high noise level in the daily life renders long-entrenched challenges to extract fECG from the combined fetal/maternal ECG signal recorded in the abdominal area of the mother. Thus, an efficient fECG extraction scheme is a dire need. In this work, we intensively explored various extraction algorithms, including template subtraction (TS), independent component analysis (ICA), and extended Kalman filter (EKF) using the data from the PhysioNet 2013 Challenge. Furthermore, the modified data with Gaussian and motion noise added, mimicking a practical scenario, were utilized to examine the performance of algorithms. Finally, we combined different algorithms together, yielding promising results, with the best performance in the F1 score of 92.61% achieved by an algorithm combining ICA and TS. With the data modified by adding different types of noise, the combination of ICA–TS–ICA showed the highest F1 score of 85.4%. It should be noted that these combined approaches required higher computational complexity, including execution time and allocated memory compared with other methods. Owing to comprehensive examination through various evaluation metrics in different extraction algorithms, this study provides insights into the implementation and operation of state-of-the-art fetal and maternal monitoring systems in the era of mobile health. 
    more » « less
  2. ; ; ; ; ; (, Human Brain Mapping)
    Abstract Data‐driven methods have been widely used in functional magnetic resonance imaging (fMRI) data analysis. They extract latent factors, generally, through the use of a simple generative model. Independent component analysis (ICA) and dictionary learning (DL) are two popular data‐driven methods that are based on two different forms of diversity—statistical properties of the data—statistical independence for ICA and sparsity for DL. Despite their popularity, the comparative advantage of emphasizing one property over another in the decomposition of fMRI data is not well understood. Such a comparison is made harder due to the differences in the modeling assumptions between ICA and DL, as well as within different ICA algorithms where each algorithm exploits a different form of diversity. In this paper, we propose the use of objective global measures, such as time course frequency power ratio, network connection summary, and graph theoretical metrics, to gain insight into the role that different types of diversity have on the analysis of fMRI data. Four ICA algorithms that account for different types of diversity and one DL algorithm are studied. We apply these algorithms to real fMRI data collected from patients with schizophrenia and healthy controls. Our results suggest that no one particular method has the best performance using all metrics, implying that the optimal method will change depending on the goal of the analysis. However, we note that in none of the scenarios we test the highly popular Infomax provides the best performance, demonstrating the cost of exploiting limited form of diversity. 
    more » « less
  3. ; ; (, International journal of mathematics and computation)
    In this paper, we develop structure assisted nonnegative matrix factorization (NMF) methods for blind source separation of degenerate data. The motivation originates from nuclear magnetic resonance (NMR) spectroscopy, where a multiple mixture NMR spectra are recorded to identify chemical compounds with similar structures. Consider the linear mixing model (LMM), we aim to identify the chemical compounds involved when the mixing process is known to be nearly singular. We first consider a class of data with dominant interval(s) (DI) where each of source signals has dominant peaks over others. Besides, a nearly singular mixing process produces degenerate mixtures. The DI condition implies clustering structures in the data points. Hence, the estimation of the mixing matrix could be achieved by data clustering. Due to the presence of the noise and the degeneracy of the data, a small deviation in the estimation may introduce errors in the output. To resolve this problem and improve robustness of the separation, methods are developed in two aspects. One is to find better estimation of the mixing matrix by allowing a constrained perturbation to the clustering output, and it can be achieved by a quadratic programming. The other is to seek sparse source signals by exploiting the DI condition, and it solves an 1 optimization. If no source information is available, we propose to adopt the nonnegative matrix factorization approach by incorporating the matrix structure (parallel columns of the mixing matrix) into the cost function and develop multiplicative iteration rules for the numerical solutions. We present experimental results of NMR data to show the performance and reliability of the method in the applications arising in NMR spectroscopy. 
    more » « less
  4. ; ; ; (, Scientific Reports)
    Independent component analysis (ICA) is a widely used blind source separation method for signal pre-processing. The determination of the number of independent components (ICs) is crucial for achieving optimal performance, as an incorrect choice can result in either under-decomposition or over-decomposition. In this study, we propose a robust method to automatically determine the optimal number of ICs, named the column-wise independent component analysis (CW_ICA). CW_ICA divides the mixed signals into two blocks and applies ICA separately to each block. A quantitative measure, derived from the rank-based correlation matrix computed from the ICs of the two blocks, is utilized to determine the optimal number of ICs. The proposed method is validated and compared with the existing determination methods using simulation and scalp EEG data. The results demonstrate that CW_ICA is a reliable and robust approach for determining the optimal number of ICs. It offers computational efficiency and can be seamlessly integrated with different ICA methods. 
    more » « less
  5. ; ; ; (, IEEE Transactions on Nanotechnology)
    Resistive Random-Access Memories (RRAM)s are considered a promising candidate for neuromorphic circuits and systems. In the letter, we investigate using TiO 2 RRAMs to solve blind source separation problem through Independent Component Analysis (ICA) for the first time. ICA has numerous uses including feature extraction. We deploy a local, unsupervised learning algorithm (error-gated Hebbian rule) to extract the independent components. The online evaluation of the weights during the training is studied taking into consideration the asymmetric nonlinear weight update behavior. The effects of the device variability are considered in the results. Finally, an example of de-mixing two Laplacian signals is given to demonstrate the efficacy of the approach. 
    more » « less
  • Citation Formats
  • MLA
  • APA
  • Chicago
  • BibTeX
  • Save / Share this Record
  • Send to Email