Variables Selection from the Patterns of the Features Applied to Spectroscopic Data—An Application Case - José L. Romero-Béjar; Francisco Javier Esquivel; José Antonio Esquivel (Mathematics)
Spectroscopic data allows for the obtaining of relevant information about the composition of samples and has been used for research in scientific disciplines such as chemistry, geology, archaeology, Mars research, pharmacy, and medicine, as well as important industrial use. In archaeology, it allows the characterization and classification of artifacts and ecofacts, the analysis of patterns, the characterization and study of the exchange of materials, etc. Spectrometers provide a large amount of data, the so-called “big data” type, which requires the use of multivariate statistical techniques, mainly principal component analysis, cluster analysis, and discriminant analysis. This work is focused on reducing the dimensionality of the data by selecting a small subset of variables to characterize the samples and presents a mathematical methodology for the selection of the most efficient variables. The objective is to identify a subset of variables based on spectral features that allow characterization of the samples under study with the least possible errors when performing quantitative analyses or discriminations between different samples. The subset is not predetermined and, in each case, is obtained for each set of samples based on the most important features of the samples under study, which allows for a good fit to the data. The reduction of the number of variables to an important performance based on the previously chosen difference between features, with a great fit to the raw data. Thus, instead of 2151 variables, a minimum optimal subset of 32 valleys and 31 peaks is obtained for a minimum difference between peaks or between valleys of 20 nm. This methodology has been applied to a sample of minerals and rocks extracted from the ECOSTRESS 1.0 spectral library.