A Fast Multi-component Latent Variable Regression Framework for Quantitative Analysis of Surface-Enhanced Raman Spectra

Abstract

Surface-enhanced Raman spectroscopy (SERS) has been a routine method for the quantitative analysis of Nano-tags or biomarkers. The multivariate calibration (MC) model is normally used to reduce the bias from the inherent instability of Raman signals. To solve the more variables than observations, ill-conditioned problem within the MC model, latent variable regression (LVR) methods are usually used. In order to decide the optimized number of latent variables (LVs) used in the model, cross-validation methods are commonly used to test every possible number, and the one gives the minimum estimated error is returned as the optimized number. In this paper we present a new multi-component LVR together with a cross-validation framework to accelerate the time-consuming processes of optimizing number of LVs. It reduces the growth rate of the algorithms from O(k^2) to O(k), where k is the possible numbers of LVs. Experimental results show the estimated results of the two frameworks are equivalent and the running time of our new framework is evidently reduced.