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2021 Scalable computational measures for entropic detection of latent relations and their applications to magnetic imaging
Illia Horenko, Davi Rodrigues, Terence O’Kane, Karin Everschor-Sitte
Commun. Appl. Math. Comput. Sci. 16(2): 267-297 (2021). DOI: 10.2140/camcos.2021.16.267


Detection of material inhomogeneities is an important task in magnetic imaging. For example, in spintronics, device efficiency is greatly impacted by sample heterogeneity. We demonstrate that the novel computationally-scalable data measures introduced in this manuscript—taking into account latent temporal relations between processes of interest—have the potential to assist current efforts to enhance the resolution of experimental techniques by providing key insights into the noisy observed data. We introduce two data relation measures—the latent dimension and the latent entropy—and analyse their mathematical and computational properties. We provide mathematical derivations of their analytic properties (e.g., monotonicity, boundedness and uniqueness) and prove the independence of the computational iteration complexity scaling of the introduced latent measures from the underlying data statistics sizes, making these measures particularly suitable for inference of latent effects in the big data applications with very large statistics sizes. Using a series of simulated and experimental magnetization data sets of increasing complexity we show that the introduced computational measures outperform considered common instruments in helping to reveal the magnetic material patterns and in the scaling of the computational cost with the data size. Introduced measures allow us to detect subtle material inhomogeneity patterns in the data which are not accessible to common data measures (like the mean, the autocorrelation and the Gaussian mixture entropy measures). For example, for a discrete heterogenous Ising model with magnetization constant anisotropy, we show that the proposed measures help to resolve exchange differences down to 1% even above the critical temperature. Furthermore, for a micromagnetic model, the latent entropy helps revealing material anisotropic inhomogeneity along components perpendicular to the main magnetization axis of the material where common data measures fail. For magneto-optical Kerr effect (MOKE) measurements, these data-driven tools can be used to visualize inhomogeneities and help to explicitly resolve impurities and pinning centres.


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Illia Horenko. Davi Rodrigues. Terence O’Kane. Karin Everschor-Sitte. "Scalable computational measures for entropic detection of latent relations and their applications to magnetic imaging." Commun. Appl. Math. Comput. Sci. 16 (2) 267 - 297, 2021.


Received: 30 October 2020; Revised: 8 April 2021; Accepted: 10 May 2021; Published: 2021
First available in Project Euclid: 29 March 2022

Digital Object Identifier: 10.2140/camcos.2021.16.267

Primary: 37M25 , 94A17
Secondary: 62H30 , 62M05

Keywords: Denoising , detection of inhomogeneities , Entropy , latent inference

Rights: Copyright © 2021 Mathematical Sciences Publishers


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Vol.16 • No. 2 • 2021
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