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