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Fig. 7 NMF results showing abundance maps a without and b with spatial smoothness constraints added.
For example, in this model (6) with spatial smoothness and sparsity, sparsity is relatively an easier constraint over spatial smoothness.
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The afterslip distribution from GPS data was estimated with the spatial smoothness constraint, while the slip estimated by similar earthquakes represents the slip in the small areas surrounding the earthquakes.
In Fig. 7, we present the NMF result with and without spatial smoothness for the ToF-SIMS data of a particular component.
The user parameter for JAFE data model is selected to the optimal values as proposed in [22] with temporal and spatial smoothness parameters, t = 2 N 3 and s = M 2, respectively.
Capturing large-scale brain systems calls for spatial regularization such as sparsity and spatial smoothness [ 35] or total-variation (TV) for piecewise smooth maps [ 36].
The proposed method is explicitly formulated as a minimization problem with an energy function that includes a data fitting term, a spatial smoothness term, and a temporal consistency term.
The spatial smoothness "prior" was specified based on Markov random fields with geographic neighbors defined as those census tracts that shared a common boundary.
For each simulation, we generated 2 whole-GM/WM maps filled with values sampled randomly from a Gaussian distribution and having the same spatial smoothness as the observed group-difference maps.
The first configuration imposes spatial smoothness on the generated mattes, while the other emphasizes background smoothness.
It relies on the inherent spatial smoothness of the data.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com