Wavelength selection using the measure of topological relevance on the self‐organizing map

Abstract

In this work, we investigated the possibility to perform wavelength selection by exploiting the metric structure of the spectrophotoscopic measurements. The topologically preserving representation of the data is performed using the self-organizing map (SOM) where the inputs' significance to the output is computed with the measure of topological relevance (MTR) on SOM. The MTR on SOM is a metric measuring the similarity between local distance matrices and we found that spectral inputs with a topology, which is, close to the output's are also associated to the wavelengths that chemically explain the influence of the spectra to the property of interest. As a result, we suggest a wavelength selection strategy based on the MTR on SOM, that is, interpretable to the domain experts and independent on the regression technique subsequently used for estimation. To support the presentation, a full-scale application from the oil refining industry is illustrated on the problem of estimating standard properties in a complex hydrocarbon product starting from spectrophotoscopic measurements. The method is further validated on the problem of octane number estimation in finished gasolines, under small sample conditions. The application led to accurate, parsimonious and understandable models. Copyright (C) 2008 John Wiley & Sons, Ltd

Comparative investigation of two different self-organizing map-based wavelength selection approaches for analysis of binary mixtures with strongly overlapping spectral lines

“…The concept of SOM is that it tries to map the similar inputs to similar or nearby map unit (neuron position or node). Two significant wavelength selection approaches based on SOM technique have been found useful in pharmaceutical field [8][9][10][11]. In general, SOM strategy can be applied in both space (sample and variable spaces).…”

“…The strategies of wavelength selection for SOM1 and SOM2 were introduced by Todeschini et al [8,9] and Corona et al [10,11], respectively. Because of the quick computation of the analysis results of enormous samples, chemometric methods for spectroscopy are still today's common multivariate method seen in in-process controlin pharmaceutical industry.…”

“…In accordance with SOM2 method, the Unifieddistance matrix (U-matrix) of each component variables (wavelength and concentration variables) were calculated independently along each direction of the data space [10]. MTR or distance (D) between each wavelengthconcentration pair of component U-matrices was estimated using Frobenius norm method as in Eq 1 [10].…”

“…MTR or distance (D) between each wavelengthconcentration pair of component U-matrices was estimated using Frobenius norm method as in Eq 1 [10].…”

“…Frobenius norm was used to determine the closeness between U-matrices. The closer to zero, the more relevant measure of two components is [10], which means that the wavelength was suitable for reconstructing the concentration. As stated by Corona et al, MTR values should be inverted (which is called topological relevance index) in order to clearly represent the relevancies, with larger values indicating stronger relevancy.…”