Institute of Physical Chemistry, Friedrich Schiller University Jena, Helmholtzweg 4, 07743, Jena, Germany.
Department of Photonic Data Science, Leibniz Institute of Photonic Technologies, Member of Leibniz Research Alliance "Leibniz-Health Technologies", Albert-Einstein-Str. 9, 07745, Jena, Germany.
Anal Bioanal Chem. 2021 Sep;413(22):5633-5644. doi: 10.1007/s00216-021-03360-1. Epub 2021 May 15.
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.
拉曼光谱数据最好用数学函数来描述；然而，由于光谱测量设置的原因，这些函数只有离散的点被测量到。因此，我们首次在函数框架内研究了拉曼光谱数据。首先，我们使用 B 样条基函数来逼近拉曼光谱。然后，我们应用了函数主成分分析，随后是线性判别分析（FPCA-LDA），并将结果与经典主成分分析随后是线性判别分析（PCA-LDA）的结果进行了比较。在这种情况下，我们使用了模拟和实验拉曼光谱。在模拟的拉曼光谱中，我们使用了正常和异常光谱来建立分类模型，其中异常光谱是通过移动一个峰位置来构建的。我们表明，FPCA-LDA 方法的平均灵敏度高于 PCA-LDA 方法的平均灵敏度，尤其是在信噪比低且峰位置移动较小的情况下。然而，对于更高的信噪比，两种方法的性能相当。此外，如果将 FPCA-LDA 方法应用于实验拉曼数据，则可以稍微提高平均灵敏度。
