Understanding the learning mechanism of convolutional neural networks in spectral analysis.

Deep learning approaches, especially convolutional neural network (CNN) models, have achieved excellent performances in vibrational spectral analysis. The critical drawback of the CNN approach is the lack of interpretation, and it is regarded as a black box. Interpreting the learning mechanism of chemometric models is critical for intuitive understanding and further application. In this study, an interpretable CNN model with a global average pooling layer is presented for Raman and mid-infrared spectral data analysis. A class activation mapping (CAM)-based approach is leveraged to visualize the active variables in the whole spectrum. The visualization of active variables shows a discriminative pattern in which the most contributed variables peaked around theoretical chemical characteristic bands. The visualization of the feature maps by three convolutional layers demonstrates the data transformation pipeline and how the CNN model hierarchically extracts informative spectral features. The first layer acts as a Savitzky-Golay filter and learns spectral shape characteristics, while the second layer learns enhanced patterns from typical spectral peaks on a few correlated variables. The third layer shows stable activations on critical spectral peaks. A partial least squares - linear discriminant analysis (PLS-LDA) model is presented for comparison on classification accuracy and model interpretation. The CNN model yields mean classification accuracies of 99.01 and 100% for E. coli and meat datasets on the test set, while the PLS-LDA models obtain accuracies of 98.83 and 100%. Both the CNN and PLS-LDA models demonstrate stable patterns on active variables while CNN models are more stable than PLS-LDA models on classification performances for various dataset partitions with Monte-Carlo cross-validation.