Using Separable Nonnegative Matrix Factorization Techniques for the Analysis of Time-Resolved Raman Spectra

The key challenge of time-resolved Raman spectroscopy is the identification of the constituent species and the analysis of the kinetics of the underlying reaction network. In this work we present an integral approach that allows for determining both the component spectra and the rate constants simultaneously from a series of vibrational spectra. It is based on an algorithm for nonnegative matrix factorization that is applied to the experimental data set following a few pre-processing steps. As a prerequisite for physically unambiguous solutions, each component spectrum must include one vibrational band that does not significantly interfere with the vibrational bands of other species. The approach is applied to synthetic “experimental” spectra derived from model systems comprising a set of species with component spectra differing with respect to their degree of spectral interferences and signal-to-noise ratios. In each case, the species involved are connected via monomolecular reaction pathways. The potential and limitations of the approach for recovering the respective rate constants and component spectra are discussed.

[1]  S. Vavasis,et al.  M L ] 7 O ct 2 01 3 Fast and Robust Recursive Algorithms for Separable Nonnegative Matrix Factorization ∗ , 2013 .

[2]  K. Neymeyr,et al.  Pure component spectral recovery and constrained matrix factorizations: concepts and applications , 2010 .

[3]  Nicolas Gillis,et al.  The Why and How of Nonnegative Matrix Factorization , 2014, ArXiv.

[4]  R I Shrager,et al.  Deconvolutions based on singular value decomposition and the pseudoinverse: a guide for beginners. , 1994, Journal of biochemical and biophysical methods.

[5]  I. Holen,et al.  Raman spectroscopic analysis differentiates between breast cancer cell lines , 2015 .

[6]  M. Keenan,et al.  Multivariate Analysis of Infrared Spectra for Monitoring and Understanding the Kinetics and Mechanisms of Adsorption Processes , 2005, Applied spectroscopy.

[7]  W. Windig,et al.  Factor Analysis in Chemistry (3rd Edition) , 2002 .

[8]  E. Henry,et al.  [8] Singular value decomposition: Application to analysis of experimental data , 1992 .

[9]  A. Soldatova,et al.  Protein dynamics from time resolved UV Raman spectroscopy. , 2008, Current opinion in structural biology.

[10]  Vikas Sindhwani,et al.  Fast Conical Hull Algorithms for Near-separable Non-negative Matrix Factorization , 2012, ICML.

[11]  A. Parker,et al.  Time-Resolved Resonance Raman Spectroscopy: Exploring Reactive Intermediates , 2011, Applied spectroscopy.

[12]  Nicolas Gillis,et al.  Fast and Robust Recursive Algorithmsfor Separable Nonnegative Matrix Factorization , 2012, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[13]  Masahiro Ando,et al.  Molecular component distribution imaging of living cells by multivariate curve resolution analysis of space-resolved Raman spectra , 2013, Journal of biomedical optics.

[14]  A. Mauk,et al.  Analysis of vibrational spectra of multicomponent systems. Application to pH-dependent resonance Raman spectra of ferricytochrome c , 1996 .

[15]  Nicolas Gillis,et al.  Successive Nonnegative Projection Algorithm for Robust Nonnegative Blind Source Separation , 2013, SIAM J. Imaging Sci..

[16]  D. E. Aston,et al.  Multivariate Analysis of Micro-Raman Spectra of Thermoplastic Polyurethane Blends Using Principal Component Analysis and Principal Component Regression , 2012, Applied spectroscopy.

[17]  M. Manfait,et al.  Identification of Raman spectroscopic markers for the characterization of normal and adenocarcinomatous colonic tissues. , 2009, Critical reviews in oncology/hematology.

[18]  Stephen A. Vavasis,et al.  On the Complexity of Nonnegative Matrix Factorization , 2007, SIAM J. Optim..

[19]  Chong-Yung Chi,et al.  A Convex Analysis Framework for Blind Separation of Non-Negative Sources , 2008, IEEE Transactions on Signal Processing.

[20]  A. Berman.  Rank Factorization of Nonnegative Matrices , 1973 .

[21]  Nicolas Gillis,et al.  Robust near-separable nonnegative matrix factorization using linear optimization , 2013, J. Mach. Learn. Res..

[22]  H. Sebastian Seung,et al.  Learning the parts of objects by non-negative matrix factorization , 1999, Nature.

[23]  Yukihiro Ozaki,et al.  Multivariate data analysis for Raman spectroscopic imaging , 2009 .

[24]  Antonio J. Plaza,et al.  Hyperspectral Unmixing Overview: Geometrical, Statistical, and Sparse Regression-Based Approaches , 2012, IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing.

[25]  Nicolas Gillis,et al.  Robustness Analysis of Hottopixx, a Linear Programming Model for Factoring Nonnegative Matrices , 2012, SIAM J. Matrix Anal. Appl..

[26]  Victoria Stodden,et al.  When Does Non-Negative Matrix Factorization Give a Correct Decomposition into Parts? , 2003, NIPS.

[27]  M. V. Van Benthem,et al.  Fast algorithm for the solution of large‐scale non‐negativity‐constrained least squares problems , 2004 .

[28]  Sanjeev Arora,et al.  Computing a nonnegative matrix factorization -- provably , 2011, STOC '12.

[29]  L. B. Thomas.  Rank Factorization of Nonnegative Matrices (A. Berman) , 1974 .

[30]  Edmund R. Malinowski,et al.  Factor Analysis in Chemistry , 1980 .