Wavelength selection using the measure of topological relevance on the Self-Organizing Map
Francesco Corona, Satu-Pia Reinikainen, Kari Aalioki, Anniki Perkkiö, Elia Liitiäinen, Roberto Baratti, Amaury Lendasse and Olli Simula
Journal of Chemometrics
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.