TY - JOUR
T1 - A semiparametric approach to source separation using independent component analysis
AU - Eloyan, Ani
AU - Ghosh, Sujit K.
N1 - Funding Information:
The authors would like to thank the editor, the associate editor and two anonymous reviewers for providing very constructive comments and guidance which have led to a much improved version of an earlier manuscript. The research of the first author was supported in part by the Grant Number R01EB012547 from the National Institute Of Biomedical Imaging And Bioengineering .
PY - 2013/2
Y1 - 2013/2
N2 - Data processing and source identification using lower dimensional hidden structure plays an essential role in many fields of applications, including image processing, neural networks, genome studies, signal processing and other areas where large datasets are often encountered. One of the common methods for source separation using lower dimensional structure involves the use of Independent Component Analysis, which is based on a linear representation of the observed data in terms of independent hidden sources. The problem thus involves the estimation of the linear mixing matrix and the densities of the independent hidden sources. However, the solution to the problem depends on the identifiability of the sources. This paper first presents a set of sufficient conditions to establish the identifiability of the sources and the mixing matrix using moment restrictions of the hidden source variables. Under such sufficient conditions a semi-parametric maximum likelihood estimate of the mixing matrix is obtained using a class of mixture distributions. The consistency of our proposed estimate is established under additional regularity conditions. The proposed method is illustrated and compared with existing methods using simulated and real datasets.
AB - Data processing and source identification using lower dimensional hidden structure plays an essential role in many fields of applications, including image processing, neural networks, genome studies, signal processing and other areas where large datasets are often encountered. One of the common methods for source separation using lower dimensional structure involves the use of Independent Component Analysis, which is based on a linear representation of the observed data in terms of independent hidden sources. The problem thus involves the estimation of the linear mixing matrix and the densities of the independent hidden sources. However, the solution to the problem depends on the identifiability of the sources. This paper first presents a set of sufficient conditions to establish the identifiability of the sources and the mixing matrix using moment restrictions of the hidden source variables. Under such sufficient conditions a semi-parametric maximum likelihood estimate of the mixing matrix is obtained using a class of mixture distributions. The consistency of our proposed estimate is established under additional regularity conditions. The proposed method is illustrated and compared with existing methods using simulated and real datasets.
KW - Constrained EM-algorithm
KW - Mixture density estimation
KW - Source identification
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U2 - 10.1016/j.csda.2012.09.012
DO - 10.1016/j.csda.2012.09.012
M3 - Article
AN - SCOPUS:84869085764
VL - 58
SP - 383
EP - 396
JO - Computational Statistics and Data Analysis
JF - Computational Statistics and Data Analysis
SN - 0167-9473
IS - 1
ER -