corr2D: Implementation of Two-Dimensional Correlation Analysis in R

In the package corr2D two-dimensional correlation analysis is implemented in R. This paper describes how two-dimensional correlation analysis is done in the package and how the mathematical equations are translated into R code. The paper features a simple tutorial with executable code for beginners, insight into at the calculations done before the correlation analysis, a detailed look at the parallelization of the fast Fourier transformation based correlation analysis and a speed test of the calculation. The package corr2D offers the possibility to preprocess, correlate and postprocess spectroscopic data using exclusively the R language. Thus, corr2D is a welcome addition to the toolbox of spectroscopists and makes two-dimensional correlation analysis more accessible and transparent.

[1]  Isao Noda,et al.  Novel developments and applications of two-dimensional correlation spectroscopy , 2016 .

[2]  B Dietzek,et al.  Molecular self-healing mechanisms between C60-fullerene and anthracene unveiled by Raman and two-dimensional correlation spectroscopy. , 2016, Physical chemistry chemical physics : PCCP.

[3]  Hadley Wickham,et al.  Tools to Make Developing R Packages Easier , 2016 .

[4]  Isao Noda,et al.  Two-Dimensional Correlation Analysis of Unevenly Spaced Spectral Data , 2003, Applied spectroscopy.

[5]  Kurt Hornik,et al.  colorspace: A Toolbox for Manipulating and Assessing Colors and Palettes , 2019, J. Stat. Softw..

[6]  Isao Noda,et al.  Two-dimensional correlation spectroscopy , 2002 .

[7]  Isao Noda,et al.  Frontiers of two-dimensional correlation spectroscopy. Part 2. Perturbation methods, fields of applications, and types of analytical probes , 2014 .

[8]  Steve Weston,et al.  Provides Foreach Looping Construct for R , 2015 .

[9]  Isao Noda,et al.  Two-dimensional infrared spectroscopy , 1989 .

[10]  Franklin E. Barton,et al.  The use of two-dimensional correlation spectroscopy to characterize instrumental differences , 2006 .

[11]  J. Tukey,et al.  An algorithm for the machine calculation of complex Fourier series , 1965 .

[12]  J. Mayr,et al.  Somewhere Over the Rainbow: How to Make Effective Use of Colors in Meteorological Visualizations , 2015 .

[13]  Yukihiro Ozaki,et al.  A New Possibility of the Generalized Two-Dimensional Correlation Spectroscopy. 2. Sample−Sample and Wavenumber−Wavenumber Correlations of Temperature-Dependent Near-Infrared Spectra of Oleic Acid in the Pure Liquid State , 2000 .

[14]  Mike Thomas,et al.  Two-dimensional FT-IR correlation analysis of the phase transitions in a liquid crystal, 4′-n-octyl-4-cyanobiphenyl (8CB) , 2000 .

[15]  Mariko Okada,et al.  Multiple Perturbation Two-Dimensional Correlation Analysis of Cellulose by Attenuated Total Reflection Infrared Spectroscopy , 2009, Applied spectroscopy.

[16]  Isao Noda,et al.  Scaling techniques to enhance two-dimensional correlation spectra , 2008 .

[17]  I. Noda Generalized Two-Dimensional Correlation Method Applicable to Infrared, Raman, and other Types of Spectroscopy , 1993 .

[18]  Isao Noda,et al.  Cyclical asynchronicity in two-dimensional (2D) correlation spectroscopy , 2006 .

[19]  Yukihiro Ozaki,et al.  New Insight into the Mathematical Background of Generalized Two-Dimensional Correlation Spectroscopy and the Influence of Mean Normalization Pretreatment on Two-Dimensional Correlation Spectra , 2001 .

[20]  Douglas W. Nychka,et al.  Tools for Spatial Data , 2016 .

[21]  Isao Noda,et al.  Graphical representation of two-dimensional correlation in vector space , 2004 .

[22]  Wei Xiong,et al.  Two-Dimensional Infrared (2D IR) Spectroscopy , 2014 .

[23]  Olaf Mersmann,et al.  Accurate Timing Functions , 2015 .

[24]  Isao Noda,et al.  Techniques useful in two-dimensional correlation and codistribution spectroscopy (2DCOS and 2DCDS) analyses , 2016 .

[25]  Royston Goodacre,et al.  Monitoring the mode of action of antibiotics using Raman spectroscopy: investigating subinhibitory effects of amikacin on Pseudomonas aeruginosa. , 2005, Analytical chemistry.

[26]  Yukihiro Ozaki,et al.  Sequential identification of model parameters by derivative double two-dimensional correlation spectroscopy and calibration-free approach for chemical reaction systems. , 2012, Analytical chemistry.

[27]  Ondřej Klobušník,et al.  ArXiv.org e-print archive , 2004 .

[28]  Yukihiro Ozaki,et al.  A New Possibility of the Generalized Two-Dimensional Correlation Spectroscopy. 1. Sample-Sample Correlation Spectroscopy , 2000 .

[29]  H. Richardson,et al.  Two-Dimensional FT-IR Correlation Analysis of the Chemisorption of Nitric Oxide on Pt(100) , 1999 .

[30]  Isao Noda,et al.  Double two-dimensional correlation analysis – 2D correlation of 2D spectra , 2010 .

[31]  Stephen Weston,et al.  Scalable Strategies for Computing with Massive Data , 2013 .

[32]  Steve Weston,et al.  Foreach Parallel Adaptor for the 'parallel' Package , 2015 .

[33]  R Core Team,et al.  R: A language and environment for statistical computing. , 2014 .

[34]  B Dietzek,et al.  Two-dimensional Raman correlation spectroscopy reveals molecular structural changes during temperature-induced self-healing in polymers based on the Diels-Alder reaction. , 2015, Physical chemistry chemical physics : PCCP.

[35]  Mirosław A. Czarnecki,et al.  Interpretation of Two-Dimensional Correlation Spectra: Science or Art? , 1998 .

[36]  A. E. Dowrey,et al.  Generalized Two-Dimensional Correlation Spectroscopy , 2000 .

[37]  Isao Noda,et al.  Close-up view on the inner workings of two-dimensional correlation spectroscopy , 2012 .

[38]  Kurt Hornik,et al.  Escaping RGBland: Selecting colors for statistical graphics , 2009, Comput. Stat. Data Anal..

[39]  J Liu,et al.  Effect of Noise on the Evaluation of Correlation Coefficients in Two-Dimensional Correlation Spectroscopy , 2003, Applied spectroscopy.

[40]  Isao Noda,et al.  Quadrature two-dimensional correlation spectroscopy (Q-2DCOS) , 2016 .

[41]  Isao Noda,et al.  Two-Dimensional Infrared (2D IR) Spectroscopy: Theory and Applications , 1990 .

[42]  Isao Noda,et al.  Frontiers of Two-Dimensional Correlation Spectroscopy. Part 1. New concepts and noteworthy developments , 2014 .

[43]  Isao Noda,et al.  Two-dimensional correlation spectroscopy (2DCOS) analysis of polynomials , 2016 .