Application of Multi-Way Analysis to 2D NMR Data

Two- and three-dimensional or even higher-dimensional NMR spectroscopy is changing from specialised techniques to more commonly used ones. As the complexity of the acquired NMR data increases, the task of analysing these data constantly becomes more and more demanding and new methods are required to facilitate the analysis. With one-dimensional NMR data multivariate data analysis has proven to be a strong tool, but how should one analyse higher-dimensional NMR data in order to extract as much relevant information as possible without having to break data down into smaller dimensions and thus lose the inherent structure? A class of multivariate data analytical techniques called multi-way analysis encompass techniques that have been designed to handle and analyse such data structures directly. In this paper, the theory of some of the most commonly used multi-way methods will be described and examples of their application to three-way arrays of NMR data reported in the literature will be given. The focus will be on the generic principles of multi-way analysis using three-way data in order to gently introduce the new concepts.

[1]  Rasmus Bro,et al.  The N-way Toolbox for MATLAB , 2000 .

[2]  H. Hotelling.  Analysis of a complex of statistical variables into principal components. , 1933 .

[3]  Timothy M. D. Ebbels,et al.  Batch statistical processing of 1H NMR‐derived urinary spectral data , 2002 .

[4]  S. Engelsen,et al.  Magnetic resonance in food science : the multivariate challenge , 2005 .

[5]  R. Bro,et al.  A new efficient method for determining the number of components in PARAFAC models , 2003 .

[6]  M. Billeter,et al.  MUNIN: A new approach to multi-dimensional NMR spectra interpretation , 2001, Journal of biomolecular NMR.

[7]  F. Rius,et al.  Graphical criterion for assessing trilinearity and selecting the optimal number of factors in the generalized rank annihilation method using liquid chromatography–diode array detection data , 2004 .

[8]  Marianne Defernez,et al.  Factors affecting the robustness of metabolite fingerprinting using 1H NMR spectra. , 2003, Phytochemistry.

[9]  Rasmus Bro,et al.  Improving the speed of multiway algorithms: Part II: Compression , 1998 .

[10]  Romà Tauler,et al.  Multivariate curve resolution applied to the analysis and resolution of two-dimensional [1H,15N] NMR reaction spectra. , 2004, Analytical chemistry.

[11]  Olav M. Kvalheim,et al.  Compression of nth‐order data arrays by B‐splines. Part 2: Application to second‐order FT‐IR spectra , 1994 .

[12]  W. Windig,et al.  Direct exponential curve resolution algorithm (DECRA): A novel application of the generalized rank annihilation method for a single spectral mixture data set with exponentially decaying contribution profiles , 1997 .

[13]  E. A. Sylvestre,et al.  Self Modeling Curve Resolution , 1971 .

[14]  H. Law.  Research methods for multimode data analysis , 1984 .

[15]  R. Bro.  PARAFAC. Tutorial and applications , 1997 .

[16]  R. Bro.  Multivariate calibration: What is in chemometrics for the analytical chemist? , 2003 .

[17]  Rasmus Bro,et al.  Analysis of lipoproteins using 2D diffusion-edited NMR spectroscopy and multi-way chemometrics , 2005 .

[18]  J. Edward Jackson,et al.  Principal Components and Factor Analysis: Part I - Principal Components , 1980 .

[19]  A. Berglund,et al.  The equilibrium unfolding of MerP characterized by multivariate analysis of 2D NMR data. , 2005, Journal of magnetic resonance.

[20]  Rasmus Bro,et al.  Multi-way Analysis with Applications in the Chemical Sciences , 2004 .

[21]  S. Wold.  Cross-Validatory Estimation of the Number of Components in Factor and Principal Components Models , 1978 .

[22]  M. K. Alam,et al.  Effect of non‐exponential and multi‐exponential decay behavior on the performance of the direct exponential curve resolution algorithm (DECRA) in NMR investigations , 2003 .

[23]  R. Bro,et al.  Multiway chemometric analysis of the metabolic response to toxins monitored by NMR , 2005 .

[24]  R. Bro.  Multiway calibration. Multilinear PLS , 1996 .

[25]  R. Bro,et al.  Towards rapid and unique curve resolution of low-field NMR relaxation data: trilinear SLICING versus two-dimensional curve fitting. , 2002, Journal of magnetic resonance.

[26]  Romà Tauler,et al.  Comparison of three‐way resolution methods for non‐trilinear chemical data sets , 2001 .

[27]  Rasmus Bro,et al.  On the difference between low-rank and subspace approximation: improved model for multi-linear PLS regression , 2001 .

[28]  R Huo,et al.  Improved DOSY NMR data processing by data enhancement and combination of multivariate curve resolution with non-linear least square fitting. , 2004, Journal of magnetic resonance.

[29]  Rasmus Bro,et al.  Chemometrics in food science—a demonstration of the feasibility of a highly exploratory, inductive evaluation strategy of fundamental scientific significance , 1998 .