Comparison of functional and discrete data analysis regimes for Raman spectra.

Area of Science:

• Spectroscopy
• Data Analysis
• Mathematical Modeling

Background:

• Raman spectral data are discrete measurements of underlying mathematical functions.
• Traditional analysis methods like principal component analysis (PCA) operate on these discrete points.
• A functional data analysis framework offers a novel approach to capture the continuous nature of spectra.

Purpose of the Study:

• To investigate Raman spectral data within a functional framework for the first time.
• To compare the performance of functional principal component analysis followed by linear discriminant analysis (FPCA-LDA) against classical PCA-LDA.
• To evaluate classification sensitivity using simulated and experimental Raman spectra.

Main Methods:

• Approximation of Raman spectra using B-spline basis functions.
• Application of functional principal component analysis (FPCA) on the approximated spectra.
• Subsequent application of linear discriminant analysis (LDA) for classification (FPCA-LDA).
• Comparison with classical PCA followed by LDA (PCA-LDA) using simulated and experimental data.

Main Results:

• FPCA-LDA demonstrated higher mean sensitivities than PCA-LDA, particularly with low signal-to-noise ratios and small peak shifts in simulated spectra.
• Both methods performed comparably at higher signal-to-noise ratios.
• A marginal improvement in mean sensitivity was observed when FPCA-LDA was applied to experimental Raman data.

Conclusions:

• The functional framework provides a more sensitive approach for Raman spectral classification compared to classical methods.
• FPCA-LDA is particularly advantageous for analyzing noisy or subtly altered spectral data.
• This functional approach holds promise for enhanced interpretation of Raman spectroscopic measurements.