13,779 research outputs found
Magnification Control in Self-Organizing Maps and Neural Gas
We consider different ways to control the magnification in self-organizing
maps (SOM) and neural gas (NG). Starting from early approaches of magnification
control in vector quantization, we then concentrate on different approaches for
SOM and NG. We show that three structurally similar approaches can be applied
to both algorithms: localized learning, concave-convex learning, and winner
relaxing learning. Thereby, the approach of concave-convex learning in SOM is
extended to a more general description, whereas the concave-convex learning for
NG is new. In general, the control mechanisms generate only slightly different
behavior comparing both neural algorithms. However, we emphasize that the NG
results are valid for any data dimension, whereas in the SOM case the results
hold only for the one-dimensional case.Comment: 24 pages, 4 figure
Rotationally-invariant mapping of scalar and orientational metrics of neuronal microstructure with diffusion MRI
We develop a general analytical and numerical framework for estimating intra-
and extra-neurite water fractions and diffusion coefficients, as well as
neurite orientational dispersion, in each imaging voxel. By employing a set of
rotational invariants and their expansion in the powers of diffusion weighting,
we analytically uncover the nontrivial topology of the parameter estimation
landscape, showing that multiple branches of parameters describe the
measurement almost equally well, with only one of them corresponding to the
biophysical reality. A comprehensive acquisition shows that the branch choice
varies across the brain. Our framework reveals hidden degeneracies in MRI
parameter estimation for neuronal tissue, provides microstructural and
orientational maps in the whole brain without constraints or priors, and
connects modern biophysical modeling with clinical MRI.Comment: 25 pages, 12 figures, elsarticle two-colum
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