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Nonlinear mixture-wise expansion approach to underdetermined blind separation of nonnegative dependent sources

Kopriva, Ivica; Jerić, Ivanka; Brkljačić, Lidija (2013) Nonlinear mixture-wise expansion approach to underdetermined blind separation of nonnegative dependent sources. Journal of Chemometrics, 27 (7/8). pp. 189-197. ISSN 0886-9383

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Abstract

Underdetermined blind separation of nonnegative dependent sources consists in decomposing set of observed mixed signals into greater number of original nonnegative and dependent component (source) signals. That is an important problem for which very few algorithms exist. It is also practically relevant for contemporary metabolic profiling of biological samples, such as biomarker identification studies, where sources (a.k.a. pure components or analytes) are aimed to be extracted from mass spectra of complex multicomponent mixtures. This paper presents method for underdetermined blind separation of nonnegative dependent sources. The method performs nonlinear mixture-wise mapping of observed data in high-dimensional reproducible kernel Hilbert space (RKHS) of functions and sparseness constrained nonnegative matrix factorization (NMF) therein. Thus, original problem is converted into new one with increased number of mixtures, increased number of dependent sources and higher-order (error) terms generated by nonlinear mapping. Provided that amplitudes of original components are sparsely distributed, that is the case for mass spectra of analytes, sparseness constrained NMF in RKHS yields, with significant probability, improved accuracy relative to the case when the same NMF algorithm is performed on original problem. The method is exemplified on numerical and experimental examples related respectively to extraction of ten dependent components from five mixtures and to extraction of ten dependent analytes from mass spectra of two to five mixtures. Thereby, analytes mimic complexity of components expected to be found in biological samples.

Item Type: Article
Additional Information: This is the peer reviewed version of the following article: Kopriva, I., Jerić, I. and Brkljačić, L. (2013), Nonlinear mixture-wise expansion approach to underdetermined blind separation of nonnegative dependent sources. J. Chemometrics, 27: 189–197. doi: 10.1002/cem.2512, which has been published in final form at http://dx.doi.org/10.1002/cem.2512. This article may be used for non-commercial purposes in accordance With Wiley Terms and Conditions for self-archiving
Uncontrolled Keywords: underdetermined blind source separation; dependent sources; reproducible kernel Hilbert spaces; empirical kernel maps; nonnegative matrix factorization
Subjects: NATURAL SCIENCES > Mathematics
NATURAL SCIENCES > Chemistry
TECHNICAL SCIENCES > Computing
Divisions: Division of Laser and Atomic Research and Development
Division of Organic Chemistry and Biochemistry
Projects:
Project titleProject leaderProject codeProject type
Nonlinear component analysis with applications in chemometrics and pathologyIvica Kopriva09.01/232MZOS
Depositing User: Ivica Kopriva
Date Deposited: 28 Apr 2015 14:23
Last Modified: 29 Apr 2015 10:24
URI: http://fulir.irb.hr/id/eprint/1796
DOI: 10.1002/cem.2512

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