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.
Keywords
detection of inhomogeneities, denoising, entropy, latent
inference