Hierarchical modelling as a gray-box approach to LIBS spectra classification

The introduction of modern machine learning approaches to Laser-Induced Breakdown Spectroscopy (LIBS) data processing has constituted a significant milestone in spectra classification. However, the complexity of these models make it hard to interpret the results in terms of the underlying spectroscopy (wavelengths and spectral lines). As a partial solution to this problem, in this paper we present a hierarchical modelling approach to spectral feature (wavelength) selection. Particularly, we propose to fit a gamma distribution in calculating the variance explained by class membership (intraclass correlation coefficient), net of other nested clustering like the specific sample, laser spots or even subsets of consecutive shots if deemed relevant. This filter approach allow us to avoid looking at all the two-way comparisons across the typically nested structure of LIBS data (class/sample/spot/shot), which quickly turns unfeasible. In order to make the results of the proposed approach as comparable as possible, the empirical application relies on the benchmark classification dataset for laser-induced breakdown spectroscopy prepared for the 2019 EMSLIBS contest. By way of comparable results with other spectroscopically explainable approach, being able to identify some 15 chemical elements from 138 samples spread across 12 classes, the paper shows the value of hierarchical modelling as a semi-automatic exploratory tool for both novice and expert spectroscopists.