Data Fusion in Action: Integrating Different Vibrational and Atomic Spectroscopy Data

Spectroscopy is a cornerstone of chemical and biological analysis, yet no single technique can fully capture the complex composition of real-world samples. Combining data from different vibrational and atomic spectroscopies provides enhanced chemical specificity, quantitative robustness, and interpretability. This tutorial introduces three major categories of multimodal data fusion: early fusion (concatenation of raw or preprocessed features), intermediate fusion (shared latent space models such as partial least squares or canonical correlation analysis), and late fusion (decision-level combination of independent models). Matrix notation is employed to formalize fusion strategies and highlight the mathematical relationships among datasets. Finally, challenges and future directions in physical interpretability, nonlinear fusion, and explainable artificial intelligence are discussed. Using a matrix-based framework, we highlight challenges in alignment, scaling, redundancy, and interpretation, and provide examples of how fusion strategies can enhance chemical analysis and diagnostics.