Essential Number of Principal Components and Nearly Training-Free Model for Spectral Analysis

TL;DR

This paper demonstrates that the number of principal components needed in spectral analysis equals the number of mixture constituents, enabling nearly training-free, fast, and accurate spectral quantification with minimal data.

Contribution

It introduces a method linking principal components directly to mixture constituents, reducing training data needs and simplifying spectral analysis.

Findings

Number of principal components equals number of constituents.

Projection from components to constituents is nearly one-to-one.

Method requires few or no training samples.

Abstract

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.