Comparison of functional and discrete data analysis regimes for Raman spectra

Interpretable One-Class Classification of Raman Spectra Using Prediction Bands Estimated by Wavelet Regression

Previously, we introduced a novel one-class classification (OCC) concept for spectra. It uses as acceptance space for genuine spectra of the target chemical, a prediction band in the wavelengths' space. As a decision rule, test spectra falling substantially outside this band are rejected as noncomplying with the target, and their deviations are documented in the wavelengths' space. This band-based OCC concept was applied to smooth signals like near-infrared (NIR) spectra. A regression model based on a smoothed principal component (PC) representation of the training spectra was used to predict unseen trajectories of future spectra. The boundaries of the most central predicted trajectories were chosen as critical trajectories. We now propose a methodology to construct a similar band-based one-class classifier for Raman spectra, which are sharper and noisier than NIR spectra. The spectra are transformed by a composition of wavelet and principal component (wPC) expansions instead of just a PC expansion in the previous methodology for NIR spectra. Wavelets can capture sharp features of Raman signals and provide a framework to efficiently denoise them. A multinormal prediction model is then used to derive predictions of future wPC scores of unseen spectra. These predicted wPC scores are then backtransformed to obtain predictions of future trajectories of unseen spectra in the wavelengths' space, whose most central region defines the acceptance band or space. This band-based one-class classifier successfully classified the first derivatives of real pharmaceutical Raman spectra, while enjoying the advantage of documenting deviations from the critical trajectories in the wavelengths' space and hence is more interpretable.