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Empirical kernel map approach to nonlinear underdetermined blind separation of sparse nonnegative dependent sources: pure component extraction from nonlinear mixture mass spectra

Kopriva, Ivica; Jerić, Ivanka; Filipović, Marko; Brkljačić, Lidija (2014) Empirical kernel map approach to nonlinear underdetermined blind separation of sparse nonnegative dependent sources: pure component extraction from nonlinear mixture mass spectra. Journal of Chemometrics, 28 (9). pp. 704-715. ISSN 0886-9383

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Abstract

Nonlinear underdetermined blind separation of nonnegative dependent sources consists in decomposing set of observed nonlinearly mixed signals into greater number of original nonnegative and dependent component (source) signals. That hard problem is practically relevant for contemporary metabolic profiling of biological samples, where sources (a.k.a. pure components or analytes) are aimed to be extracted from mass spectra of nonlinear multicomponent mixtures. This paper presents method for nonlinear underdetermined blind separation of nonnegative dependent sources that comply with sparse probabilistic model, i.e. sources are constrained to be sparse in support and amplitude. That model is validated on experimental pure components mass spectra. Under sparse prior nonlinear problem is converted into equivalent linear one comprised of original sources and their higher-, mostly second, order monomials. Influence of these monomials, that stand for error terms, is reduced by preprocessing matrix of mixtures by means of robust principal component analysis, hard-, soft- and trimmed thresholding. Preprocessed data matrices are mapped in high-dimensional reproducible kernel Hilbert space (RKHS) of functions by means of empirical kernel map. Sparseness constrained nonnegative matrix factorizations (NMF) in RKHS yield sets of separated components. They are assigned to pure components from the library using maximal correlation criterion. The methodology is exemplified on demanding numerical and experimental examples related respectively to extraction of 8 dependent components from 3 nonlinear mixtures and to extraction of 25 dependent analytes from 9 nonlinear mixtures mass spectra recorded in nonlinear chemical reaction of peptide synthesis.

Item Type: Article
Additional Information: This is the peer reviewed version of the following article: Kopriva I., Jerić I., Filipović M. and Brkljačić L. (2014), Empirical kernel map approach to nonlinear underdetermined blind separation of sparse nonnegative dependent sources: pure component extraction from nonlinear mixture mass spectra, Journal of Chemometrics, 28, pages 704–715, doi: 10.1002/cem.2635, which has been published in final form at http://dx.doi.org/10.1002/cem.2635. This article may be used for non-commercial purposes in accordance With Wiley Terms and Conditions for self-archiving
Uncontrolled Keywords: nonlinear underdetermined blind source separation; robust principal component analysis; thresholding,; 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 14:32
Last Modified: 28 Oct 2015 00:15
URI: http://fulir.irb.hr/id/eprint/1794
DOI: 10.1002/cem.2635

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