Application of Raman dispersion spectroscopy in 3‐way multivariate data analysis

Abstract

In this paper a new application of Raman dispersion spectroscopy (RADIS) is proposed, namely as a source of 3-way data in multivariate analysis of classification problems, i.e. problems where different molecular species are identified in a number of samples. Owing to the coherent nature of the absorption-emission sequence in the Raman process, the unpolarized data generated by RADIS are born as 3-way multivariate data. To demonstrate the potential of RADIS, a series of classification problems have been constructed and analyzed. By using computer-simulated Raman and RADIS data it is shown that the 3-way RADIS data obtained from very few samples, using only a few laser frequencies and a few Raman bands, can in general provide highly reliable results in classification problems without any a priori knowledge about the number of different molecular species in the samples. Quantitative comparisons have been made between a principal component analysis (PCA) of the 2-way Raman data and a Tucker 3 analysis of the corresponding 3-way RADIS data. It is found that the 3-way RADIS data will give rise to a recognition ratio equal to 100% even in the worst case where no conclusions about the number of different molecular species in the samples can be drawn from the PCA of the 2-way Raman data. It is shown that only the raw RADIS data are needed for the multivariate analysis, so that the use of internal standards, corrections for self-absorption and other corrections necessary in molecular dynamics problems can be avoided. The results do not depend very much on the particular excitation wavenumbers used. Furthermore in most cases the fluorescence background does not influence the results. These facts together with the increased availability of solid state lasers with a variety of wavenumbers makes it easy to implement the proposed application of RADIS in practice.

Raman Spectroscopy: A Non-Destructive and On-Site Tool for Control of Food Quality?

“…Details about performing the Tucker analysis on similar RADIS data are given in Hedegaard & Hassing (2008). In both the PCA and in the Tucker 3 analysis the classification succeeds and the results are comparable, since the ratios between the average distance between the two classes and the variation within each class are similar.…”

“…A discussion of the mathematical details of applying Tucker 3 on various kind of spectroscopic data can be found in A. K. Smilde & Geladi (2004). Tucker 3 has proven most useful, when compared to other 3-way models, for treating Raman based data A. K. Smilde & Geladi (2004); Hedegaard & Hassing (2008), which is caused by the high quality of the "molecular bar codes" produced in both dimensions of the RADIS data matrix. In the Tucker 3 model, the elements of the data matrix can be expressed as:…”

Solving chemical classification problems using polarized Raman data

“…The three-way method in Ref. [7] utilizes this by combining the REP's with the corresponding Raman spectrum.…”

“…[3] Typically, the spectroscopic data are two-way data collected in a data matrix, where each element contains the intensity measured at a certain wavenumber for a specific sample. Because, as mentioned, the data are often analyzed by using PCA, a brief introduction will be given in the following section, a thorough explanation of the method can be found in Refs [7,8]. The Raman spectra of N S samples are measured with an appropriate excitation wavenumber.…”

“…[5,6] In Ref. [7], a three-way multivariate method is discussed, which benefits from the fact that the Raman process can be regarded as a coherent absorption-emission sequence. This has the consequence that when a few unpolarized Raman spectra are measured with different excitation wavenumbers in the pre-resonance or resonance region of an allowed electronic transition, the Raman data are automatically born as three-way data.…”