Essential Number of Principal Components and Nearly Training-Free Model for Spectral Analysis
This provides a simplified and efficient solution for spectral quantification in multi-gas analysis, though it appears incremental as it builds on existing principal component methods.
The paper tackles the problem of determining the number of principal components needed for spectral analysis of multi-gas mixtures, showing that it equals the number of independent constituents, which simplifies quantification and enables a nearly training-free model with fast and accurate results.
Through a study of multi-gas mixture datasets, we show that in multi-component spectral analysis, the number of functional or non-functional principal components required to retain the essential information is the same as the number of independent constituents in the mixture set. Due to the mutual in-dependency among different gas molecules, near one-to-one projection from the principal component to the mixture constituent can be established, leading to a significant simplification of spectral quantification. Further, with the knowledge of the molar extinction coefficients of each constituent, a complete principal component set can be extracted from the coefficients directly, and few to none training samples are required for the learning model. Compared to other approaches, the proposed methods provide fast and accurate spectral quantification solutions with a small memory size needed.