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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:
 [1];  [1]; ORCiD logo [1]; ORCiD logo [2]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
  2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Univ. of New Mexico, Albuquerque, NM (United States). Comprehensive Cancer Center
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) (SC-23); 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
Grant/Contract Number:  
AC52-06NA25396; 11145687; 20180060
Resource Type:
Journal Article: Published Article
Journal Name:
PLoS ONE
Additional Journal Information:
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., and Alexandrov, Boian S. 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. 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., and Alexandrov, Boian S. 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.},
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 = {Thu Mar 08 00:00:00 EST 2018},
month = {Thu Mar 08 00:00:00 EST 2018}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at 10.1371/journal.pone.0193974

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