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Title: Nonnegative Matrix Factorization for identification of unknown number of sources emitting delayed signals

Abstract

Factor analysis is broadly used as a powerful unsupervised machine learning tool for reconstruction of hidden features in recorded mixtures of signals. In the case of a linear approximation, the mixtures can be decomposed by a variety of model-free Blind Source Separation (BSS) algorithms. Most of the available BSS algorithms consider an instantaneous mixing of signals, while the case when the mixtures are linear combinations of signals with delays is less explored. Especially difficult is the case when the number of sources of the signals with delays is unknown and has to be determined from the data as well. To address this problem, here, we present a new method based on Nonnegative Matrix Factorization (NMF) that is capable of identifying: (a) the unknown number of the sources, (b) the delays and speed of propagation of the signals, and (c) the locations of the sources. Our method can be used to decompose records of mixtures of signals with delays emitted by an unknown number of sources in a nondispersive medium, based only on recorded data. This is the case, for example, when electromagnetic signals from multiple antennas are received asynchronously; or mixtures of acoustic or seismic signals recorded by sensors locatedmore » at different positions; or when a shift in frequency is induced by the Doppler effect. By applying our method to synthetic datasets, we demonstrate its ability to identify the unknown number of sources as well as the waveforms, the delays, and the strengths of the signals. Using Bayesian analysis, we also evaluate estimation uncertainties and identify the region of likelihood where the positions of the sources can be found.« less

Authors:
; ; ; ORCiD logo;
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Biological and Environmental Research (BER); USDOE Laboratory Directed Research and Development (LDRD) Program
OSTI Identifier:
1424824
Alternate Identifier(s):
OSTI ID: 1459818
Report Number(s):
LA-UR-16-27232
Journal ID: ISSN 1932-6203; 10.1371/journal.pone.0193974
Grant/Contract Number:  
AC52-06NA25396; 11145687; 20180060
Resource Type:
Published Article
Journal Name:
PLoS ONE
Additional Journal Information:
Journal Name: PLoS ONE Journal Volume: 13 Journal Issue: 3; Journal ID: ISSN 1932-6203
Publisher:
Public Library of Science
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; seismic signal processing; acoustic signals; algorithms; bayesian method; approximation methods; electromagnetic radiation; mixtures; sound waves

Citation Formats

Iliev, Filip L., Stanev, Valentin G., Vesselinov, Velimir V., Alexandrov, Boian S., and Zhang, Le. Nonnegative Matrix Factorization for identification of unknown number of sources emitting delayed signals. United States: N. p., 2018. Web. doi:10.1371/journal.pone.0193974.
Iliev, Filip L., Stanev, Valentin G., Vesselinov, Velimir V., Alexandrov, Boian S., & Zhang, Le. Nonnegative Matrix Factorization for identification of unknown number of sources emitting delayed signals. United States. doi:10.1371/journal.pone.0193974.
Iliev, Filip L., Stanev, Valentin G., Vesselinov, Velimir V., Alexandrov, Boian S., and Zhang, Le. Thu . "Nonnegative Matrix Factorization for identification of unknown number of sources emitting delayed signals". United States. doi:10.1371/journal.pone.0193974.
@article{osti_1424824,
title = {Nonnegative Matrix Factorization for identification of unknown number of sources emitting delayed signals},
author = {Iliev, Filip L. and Stanev, Valentin G. and Vesselinov, Velimir V. and Alexandrov, Boian S. and Zhang, Le},
abstractNote = {Factor analysis is broadly used as a powerful unsupervised machine learning tool for reconstruction of hidden features in recorded mixtures of signals. In the case of a linear approximation, the mixtures can be decomposed by a variety of model-free Blind Source Separation (BSS) algorithms. Most of the available BSS algorithms consider an instantaneous mixing of signals, while the case when the mixtures are linear combinations of signals with delays is less explored. Especially difficult is the case when the number of sources of the signals with delays is unknown and has to be determined from the data as well. To address this problem, here, we present a new method based on Nonnegative Matrix Factorization (NMF) that is capable of identifying: (a) the unknown number of the sources, (b) the delays and speed of propagation of the signals, and (c) the locations of the sources. Our method can be used to decompose records of mixtures of signals with delays emitted by an unknown number of sources in a nondispersive medium, based only on recorded data. This is the case, for example, when electromagnetic signals from multiple antennas are received asynchronously; or mixtures of acoustic or seismic signals recorded by sensors located at different positions; or when a shift in frequency is induced by the Doppler effect. By applying our method to synthetic datasets, we demonstrate its ability to identify the unknown number of sources as well as the waveforms, the delays, and the strengths of the signals. Using Bayesian analysis, we also evaluate estimation uncertainties and identify the region of likelihood where the positions of the sources can be found.},
doi = {10.1371/journal.pone.0193974},
journal = {PLoS ONE},
number = 3,
volume = 13,
place = {United States},
year = {2018},
month = {3}
}

Journal Article:
Free Publicly Available Full Text
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DOI: 10.1371/journal.pone.0193974

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Works referenced in this record:

Shifted factor analysis?Part II: Algorithms
journal, January 2003

  • Hong, Sungjin; Harshman, Richard A.
  • Journal of Chemometrics, Vol. 17, Issue 7
  • DOI: 10.1002/cem.809

A blind source separation technique using second-order statistics
journal, January 1997

  • Belouchrani, A.; Abed-Meraim, K.; Cardoso, J. -F.
  • IEEE Transactions on Signal Processing, Vol. 45, Issue 2
  • DOI: 10.1109/78.554307

Robust adaptive Metropolis algorithm with coerced acceptance rate
journal, August 2011


Shifted factor analysis?Part I: Models and properties
journal, January 2003

  • Harshman, Richard A.; Hong, Sungjin; Lundy, Margaret E.
  • Journal of Chemometrics, Vol. 17, Issue 7
  • DOI: 10.1002/cem.808

Shifted Non-Negative Matrix Factorization
conference, August 2007

  • Morup, Morten; Madsen, Kristoffer H.; Hansen, Lars K.
  • 2007 IEEE Workshop on Machine Learning for Signal Processing
  • DOI: 10.1109/MLSP.2007.4414296

The Representation and Matching of Pictorial Structures
journal, January 1973

  • Fischler, M. A.; Elschlager, R. A.
  • IEEE Transactions on Computers, Vol. C-22, Issue 1
  • DOI: 10.1109/T-C.1973.223602

Business Intelligence and Analytics: From Big Data to Big Impact
journal, January 2012


Non-negative matrix factorization for polyphonic music transcription
conference, January 2003

  • Smaragdis, P.; Brown, J. C.
  • 2003 IEEE Workshop on Applications of Signal Processing to Audio and Acoustics (IEEE Cat. No.03TH8684)
  • DOI: 10.1109/ASPAA.2003.1285860

Dynamical Model of Drug Accumulation in Bacteria: Sensitivity Analysis and Experimentally Testable Predictions
journal, November 2016


Statistical Theory of Passive Location Systems
journal, March 1984

  • Torrieri, Don
  • IEEE Transactions on Aerospace and Electronic Systems, Vol. AES-20, Issue 2
  • DOI: 10.1109/TAES.1984.310439

An Approach to Bayesian Sensitivity Analysis
journal, November 1996


Signatures of mutational processes in human cancer
journal, August 2013

  • Alexandrov, Ludmil B.; Nik-Zainal, Serena; Wedge, David C.
  • Nature, Vol. 500, Issue 7463
  • DOI: 10.1038/nature12477

Silhouettes: A graphical aid to the interpretation and validation of cluster analysis
journal, November 1987


Interpolation in Time Series: An Introductive Overview of Existing Methods, Their Performance Criteria and Uncertainty Assessment
journal, October 2017

  • Lepot, Mathieu; Aubin, Jean-Baptiste; Clemens, François
  • Water, Vol. 9, Issue 10
  • DOI: 10.3390/w9100796

Blind source separation for groundwater pressure analysis based on nonnegative matrix factorization
journal, September 2014

  • Alexandrov, Boian S.; Vesselinov, Velimir V.
  • Water Resources Research, Vol. 50, Issue 9
  • DOI: 10.1002/2013WR015037

Learning the parts of objects by non-negative matrix factorization
journal, October 1999

  • Lee, Daniel D.; Seung, H. Sebastian
  • Nature, Vol. 401, Issue 6755
  • DOI: 10.1038/44565

What makes Big Data, Big Data? Exploring the ontological characteristics of 26 datasets
journal, January 2016


Least square solutions of energy based acoustic source localization problems
conference, January 2004

  • Li, D.
  • Workshops on Mobile and Wireless Networking/High Performance Scientific, Engineering Computing/Network Design and Architecture/Optical Networks Control and Management/Ad Hoc and Sensor Networks/Compile and Run Time Techniques for Parallel Computing ICPP 2004
  • DOI: 10.1109/ICPPW.2004.1328053

Probabilistic sensitivity analysis of complex models: a Bayesian approach
journal, August 2004

  • Oakley, Jeremy E.; O'Hagan, Anthony
  • Journal of the Royal Statistical Society: Series B (Statistical Methodology), Vol. 66, Issue 3
  • DOI: 10.1111/j.1467-9868.2004.05304.x