A comparative study of point-to-point algorithms for matching spectra

Abstract

Matching spectra is necessary for database searches, assessing the source of an unknown sample, structure elucidation, and classification of spectra. A direct method of matching is to compare, point by point, two digitized spectra, the outcome being a parameter which quantifies the degree of similarity or dissimilarity between the spectra. Examples studied here are correlation coefficient squared, and Euclidean cosine squared, both applied to the raw spectra and first difference values of absorbance. It is shown that spectra do not fulfill the requirements for a normal statistical interpretation of the correlation coefficient; in particular they are not normally distributed variables. It is therefore not correct to use a Student-t test to calculate the probability of the null hypothesis that two spectra are not correlated on the basis of a correlation coefficient between them. We have investigated the effect on the similarity indices, of systematically changing the mean and standard deviation of a single Gaussian peak relative to a reference Gaussian peak; and of changing one peak, and of changing many peaks, in a simulated ten-peak spectrum. Squared Euclidean cosine is least sensitive to changes and the first difference methods are most sensitive to changes in mean and standard deviation of peaks. A shift of the center of a peak has a greater effect on the indices than increases in peak width, but a decrease in peak width does lead to significant changes in the indices. We recommend that if these indices are to be used to match spectra, appropriate windows should be chosen to avoid dilution by regions with no significant change.

On the interpretation of the Raman spectra of Maya Blue: a review on the literature data

“…A direct method of matching is to compare, point by point, two digitised spectra, the outcome being a parameter that quantifies the degree of similarity or dissimilarity between the spectra. In view of problems associated with correlations via the conventional Student t-test, [60] the similarity between spectra was calculated from hierarchical cluster analysis with Euclidean distance of the auto-scaled (normalised) peak intensities (vide infra). A graphical view of spectrum-to-spectrum similarity can be obtained from the correlation coefficients in two-intensity diagrams such as in Fig.…”

Spectral matching approaches in hyperspectral image processing

“…A low-quality library includes noisy and contaminated query spectra. In a study of point-to-point pattern matching, Li et al (2006) stated that even a correlation coefficient of r = 0.99 does not mean a match in all situations. It is the analyst's responsibility to decide whether the spectral match corresponds to the real situation.…”

“…The small informative peaks and overlapped peaks in the spectra cannot be easily identified by the software and hence the shape of the peak cannot be described accurately. To overcome this difficulty, point-to-point matching algorithms were developed where all the points in the spectra are used (Li et al 2006). Lau, Hon, and Bai (2000) developed the Effective Peak Matching technique where the positions of three peaks in the sample spectrum are compared to the three largest peaks in the selected reference spectrum.…”

A new algorithm for identification of components in a mixture: application to Raman spectra of solid amino acids

“…Li et al 13 dealt with the general analysis of the correlation coefficient, Euclidean cosine and their rst-difference counterparts applied to simulated spectra of one peak and ten peaks. The authors studied the inuence of changing peak width and peak position on the similarity (dissimilarity) indices.…”