Comparison of functional and discrete data analysis regimes for Raman spectra

Raman spectral data are best described by mathematical functions; however, due to the spectroscopic measurement setup, only discrete points of these functions are measured. Therefore, we investigated the Raman spectral data for the first time in the functional framework. First, we approximated the Raman spectra by using B-spline basis functions. Afterwards, we applied the functional principal component analysis followed by the linear discriminant analysis (FPCA-LDA) and compared the results with those of the classical principal component analysis followed by the linear discriminant analysis (PCA-LDA). In this context, simulation and experimental Raman spectra were used. In the simulated Raman spectra, normal and abnormal spectra were used for a classification model, where the abnormal spectra were built by shifting one peak position. We showed that the mean sensitivities of the FPCA-LDA method were higher than the mean sensitivities of the PCA-LDA method, especially when the signal-to-noise ratio is low and the shift of the peak position is small. However, for a higher signal-to-noise ratio, both methods performed equally. Additionally, a slight improvement of the mean sensitivity could be shown if the FPCA-LDA method was applied to experimental Raman data.

Automated summary

In this study, Raman spectral data were analyzed using B-spline basis functions for approximation, followed by functional principal component analysis and linear discriminant analysis (FPCA-LDA) compared to classical PCA-LDA. Results showed that FPCA-LDA had higher mean sensitivities than PCA-LDA, especially with low signal-to-noise ratio and small peak shifts. However, both methods performed equally with higher signal-to-noise ratio, and a slight improvement was observed when FPCA-LDA was applied to experimental Raman data.