Quaternion-based Parallel Feature Extraction: Extending the Horizon of Quantitative Analysis using TLC-SERS Sensing

Quantitative analysis using thin-layer chromatography coupled in tandem with surface-enhanced Raman scattering (TLC-SERS) still remains a grand challenge due to many uncontrollable variations during the TLC developing process and the random nature of the SERS substrates. Traditional chemometric methods solve this problem by sampling multiple SERS spectra in the sensing spot and then conducting statistical analysis of the SERS signals to mitigate the variation of quantitative analysis, while still ignoring the spatial distribution of the target species and the correlation among the multiple sampling points. In this paper, we proposed for the first time a parallel feature extraction and fusion method based on quaternion signal processing techniques, which can enable quantitative analysis using recently established TLC-SERS techniques. By marking three deterministic sampling points, we recorded spatially correlated SERS spectra to constitute an integral representation model of triple-spectra by a pure quaternion matrix. Quaternion principal component analysis (QPCA) was utilized for features extraction and followed by feature crossing among the quaternion principal components to obtain final fusion spectral feature vectors. Support vector regression (SVR) was then used to establish the quantitative model of melamine-contaminated milk samples with seven concentrations (1ppm to 250ppm). Compared with traditional TLC-SERS analysis methods, QPCA method significantly improved the accuracy of quantification by reaching only 7% and 2% quantization errors at 20 and 105 ppm concentration. Validation testing based on reasonable amount of statistic measurement results showed consistently smaller measurement errors and variance, which proved the effectiveness of QPCA method for TLC-SERS based quantitative sensing applications.