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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-massiveblack holes. Two competing physical models, one whose variable components areadditive and the other whose variable components are multiplicative, are knownto successfully describe X-ray spectral variation of these super-massive blackholes, within accuracy of the contemporary observation. We hope to utilizethese techniques to compare the viability of the models by probing themathematical structure of the observed spectra, while comparing advantages anddisadvantages of each technique. We find that PCA is best to determine thedimensionality of a dataset, while NMF is better suited for interpretingspectral components and comparing them in terms of the physical models inquestion. ICA is able to reconstruct the parameters responsible for spectralvariation. In addition, we find that the results of these techniques aresufficiently different that applying them to observed data may be a useful testin comparing the accuracy of the two spectral models.

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