Exploring Important Features in Continuous Spectral Datasets Using Supervised Learning

Spectral characterization and analysis of materials often involve examining large, complex, multidimensional data sets that require both time and domain experience. Supervised learning methods are exceptionally useful for identifying the most relevant features or descriptors in labeled data sets. Key features that modulate the predicted property discriminate against different data categories/labels or magnitudes, providing insights into the complex relationships between features and modeled properties, so-called quantitative structure-property relationships. In this work, we report regression machine learning (ML) models trained on spectroscopic data sets from time-of-flight secondary ion mass spectrometry (ToF-SIMS) and small-angle X-ray scattering (SAXS). We employed the least absolute shrinkage and selection operator (LASSO), partial least squares (PLS), random forest (RF), one-dimensional convolutional neural network (1D-CNN), and multilayer perceptron (MLP) algorithms. We investigated the ability of the ML methods to model large or noisy, continuous spectral data and to elucidate important features controlling the response variable. This was achieved by computing feature attribution measures relevant to each method (e.g., regression coefficients for LASSO and PLS, out-of-bag permuted feature importance for RF, and the gradient-weighted class activation mapping (Grad-CAM) for the 1D-CNN). We report their performance quantitatively using a nested k-fold cross-validation approach to comprehensively evaluate the training and test errors. The results indicate that RF and the 1D-CNN outperformed their linear counterparts, while the MLP underperformed. Additionally, we explored how changing the CNN architecture affected its translation-invariance property and interactions with the position-invariant SIMS and noninvariant SAXS data, providing further insights into the utility of these methods.