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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.…
Autor*innen: | R. Sechi, K. Fackeldey, Surahit ChewleORCiD, M. Weber |
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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): | Creative 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 |