SepFree NMF: A Toolbox for Analyzing the Kinetics of Sequential Spectroscopic Data

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dc.contributor.authorSechi, Renata
dc.contributor.authorFackeldey, Konstantin
dc.contributor.authorChewle, Surahit
dc.contributor.authorWeber, Marcus
dc.date.accessioned2022-09-19T11:40:25Z
dc.date.available2022-09-19T11:40:25Z
dc.date.issued2022-08-24
dc.date.updated2022-09-07T13:22:22Z
dc.description.abstractThis work addresses the problem of determining the number of components from sequential spectroscopic data analyzed by non-negative matrix factorization without separability assumption (SepFree NMF). These data are stored in a matrix M of dimension “measured times” versus “measured wavenumbers” and can be decomposed to obtain the spectral fingerprints of the states and their evolution over time. SepFree NMF assumes a memoryless (Markovian) process to underline the dynamics and decomposes M so that M=WH, with W representing the components’ fingerprints and H their kinetics. However, the rank of this decomposition (i.e., the number of physical states in the process) has to be guessed from pre-existing knowledge on the observed process. We propose a measure for determining the number of components with the computation of the minimal memory effect resulting from the decomposition; by quantifying how much the obtained factorization is deviating from the Markovian property, we are able to score factorizations of a different number of components. In this way, we estimate the number of different entities which contribute to the observed system, and we can extract kinetic information without knowing the characteristic spectra of the single components. This manuscript provides the mathematical background as well as an analysis of computer generated and experimental sequentially measured Raman spectra.en
dc.description.sponsorshipDFG, 390685689, EXC 2046: MATH+: Berlin Mathematics Research Centeren
dc.identifier.eissn1999-4893
dc.identifier.urihttps://depositonce.tu-berlin.de/handle/11303/17497
dc.identifier.urihttp://dx.doi.org/10.14279/depositonce-16278
dc.language.isoenen
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/en
dc.subject.ddc150 Psychologiede
dc.subject.otherkinetics from experimentsen
dc.subject.otherseparability assumptionen
dc.subject.othersequential spectroscopic dataen
dc.titleSepFree NMF: A Toolbox for Analyzing the Kinetics of Sequential Spectroscopic Dataen
dc.typeArticleen
dc.type.versionpublishedVersionen
dcterms.bibliographicCitation.articlenumber297en
dcterms.bibliographicCitation.doi10.3390/a15090297en
dcterms.bibliographicCitation.issue9en
dcterms.bibliographicCitation.journaltitleAlgorithmsen
dcterms.bibliographicCitation.originalpublishernameMDPIen
dcterms.bibliographicCitation.originalpublisherplaceBaselen
dcterms.bibliographicCitation.volume15en
tub.accessrights.dnbfreeen
tub.affiliationFak. 2 Mathematik und Naturwissenschaften::Inst. Mathematik::FG Modellierung, Simulation und Optimierung in Natur- und Ingenieurwissenschaftende
tub.affiliation.facultyFak. 2 Mathematik und Naturwissenschaftende
tub.affiliation.groupFG Modellierung, Simulation und Optimierung in Natur- und Ingenieurwissenschaftende
tub.affiliation.instituteInst. Mathematikde
tub.publisher.universityorinstitutionTechnische Universität Berlinen

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