Models and Methods for Quantitative Analysis of Surface-Enhanced Raman Spectra

The quantitative analysis of surface-enhanced Raman spectra using scattering nanoparticles has shown the potential and promising applications in in vivo molecular imaging. The diverse approaches have been used for quantitative analysis of Raman spectra information, which can be categorized as direct classical least squares models, full spectrum multivariate calibration models, selected multivariate calibration models, and latent variable regression (LVR) models. However, the working principle of these methods in the Raman spectra application remains poorly understood and a clear picture of the overall performance of each model is missing. Based on the characteristics of the Raman spectra, in this paper, we first provide the theoretical foundation of the aforementioned commonly used models and show why the LVR models are more suitable for quantitative analysis of the Raman spectra. Then, we demonstrate the fundamental connections and differences between different LVR methods, such as principal component regression, reduced-rank regression, partial least square regression (PLSR), canonical correlation regression, and robust canonical analysis, by comparing their objective functions and constraints. We further prove that PLSR is literally a blend of multivariate calibration and feature extraction model that relates concentrations of nanotags to spectrum intensity. These features (a.k.a. latent variables) satisfy two purposes: the best representation of the predictor matrix and correlation with the response matrix. These illustrations give a new understanding of the traditional PLSR and explain why PLSR exceeds other methods in quantitative analysis of the Raman spectra problem. In the end, all the methods are tested on the Raman spectra datasets with different evaluation criteria to evaluate their performance.