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

arXiv: https://arxiv.org/abs/2212.14623 · HTML: https://mlsanity.com/paper/2212.14623/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 46 references that are in the map.
- First posted on arXiv 30 Dec 2022.

## Builds on (most cited first, 4 of 4)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [An Introduction to Convolutional Neural Networks](https://mlsanity.com/paper/1511.08458/) (2015)
- [Deep Learning for Computational Chemistry](https://mlsanity.com/paper/1701.04503/) (2017)
- [Multi-label Classification with Optimal Thresholding for Multi-composition Spectroscopic Analysis](https://mlsanity.com/paper/1906.10242/) (2019)

## Abstract (arXiv)

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.