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SepFree NMF: A toolbox for analyzing the kinetics of sequential spectroscopic data

  • This 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 toThis 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.zeige mehrzeige weniger

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Metadaten
Autor*innen:R. Sechi, K. Fackeldey, Surahit ChewleORCiD, M. Weber
Dokumenttyp:Zeitschriftenartikel
Veröffentlichungsform:Verlagsliteratur
Sprache:Englisch
Titel des übergeordneten Werkes (Englisch):Algorithms
Jahr der Erstveröffentlichung:2022
Organisationseinheit der BAM:6 Materialchemie
6 Materialchemie / 6.3 Strukturanalytik
Veröffentlichende Institution:Bundesanstalt für Materialforschung und -prüfung (BAM)
Verlag:MDPI
Verlagsort:Basel
Jahrgang/Band:15
Ausgabe/Heft:9
Aufsatznummer:297
Erste Seite:1
Letzte Seite:16
DDC-Klassifikation:Naturwissenschaften und Mathematik / Chemie / Analytische Chemie
Technik, Medizin, angewandte Wissenschaften / Ingenieurwissenschaften / Ingenieurwissenschaften und zugeordnete Tätigkeiten
Freie Schlagwörter:Kinetics from experiments; Separability assumption; Sequential spectroscopic data
Themenfelder/Aktivitätsfelder der BAM:Chemie und Prozesstechnik
Material
DOI:10.3390/a15090297
URN:urn:nbn:de:kobv:b43-559046
ISSN:1999-4893
Verfügbarkeit des Dokuments:Datei für die Öffentlichkeit verfügbar ("Open Access")
Lizenz (Deutsch):License LogoCreative Commons - CC BY - Namensnennung 4.0 International
Datum der Freischaltung:05.10.2022
Referierte Publikation:Ja
Datum der Eintragung als referierte Publikation:05.10.2022
Schriftenreihen ohne Nummerierung:Wissenschaftliche Artikel der BAM
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