Probabilistic Partial Least Square Regression: A Robust Model for Quantitative Analysis of Raman Spectroscopy Data

Raman spectroscopy has been one of the most sensitive techniques widely used in chemical and pharmaceutical material identification research ever since it is invented based on Raman scattering theory, because of the fingerprints property of Raman signals to different materials. With the latest development of surface enhanced Raman scattering (SERS) nanoparticles, Raman spectroscopy is now used in more and more quantitative analysis applications. But due to the unavoidable instable problem of Raman spectroscopy signal, as well as the high signal dimension and small sample number problem, it is badly in need of a robust and accurate signal quantitative analysis method. Based on Partial Least Square Regression (PLSR) method, Probabilistic PCA and Probabilistic curve-fitting idea, we propose a new Probabilistic-PLSR (PPLSR) model. It explains PLSR from a probabilistic viewpoint and deeply describes the physical meaning of PLSR model. It is a solid foundation to develop more robust and accurate probabilistic PLSR models with Bayesian model in order to solve the over-fitting problem. And since this model adds a regularization term in the matrix of regression coefficients, the estimated result is more robust than PLSR model. We also provide an EM Algorithm to estimate the parameters of the model from sample data. To take fully use of the valuable data, we design two experiments, leave-one-out and cross-validation-on-average-signal, on one real Raman spectroscopy signal data set. By comparing with results from traditional Least Square (LS) method and traditional PLSR, we demonstrate PPLSR is more robust and accurate.