Application of data science techniques to disentangle X-ray spectral variation of super-massive black holes

TL;DR

This study applies NMF, PCA, and ICA data science techniques to simulated X-ray spectra of super-massive black holes to evaluate and compare physical models of spectral variation.

Contribution

It demonstrates how different data analysis methods can distinguish between additive and multiplicative spectral models in black hole X-ray data.

Findings

PCA effectively determines data dimensionality.

NMF aids in interpreting spectral components.

ICA reconstructs spectral variation parameters.

Abstract

We apply three data science techniques, Nonnegative Matrix Factorization (NMF), Principal Component Analysis (PCA) and Independent Component Analysis (ICA), to simulated X-ray energy spectra of a particular class of super-massive black holes. Two competing physical models, one whose variable components are additive and the other whose variable components are multiplicative, are known to successfully describe X-ray spectral variation of these super-massive black holes, within accuracy of the contemporary observation. We hope to utilize these techniques to compare the viability of the models by probing the mathematical structure of the observed spectra, while comparing advantages and disadvantages of each technique. We find that PCA is best to determine the dimensionality of a dataset, while NMF is better suited for interpreting spectral components and comparing them in terms of the physical models in question. ICA is able to reconstruct the parameters responsible for spectral variation. In addition, we find that the results of these techniques are sufficiently different that applying them to observed data may be a useful test in comparing the accuracy of the two spectral models.