Self-organization in the brain: Structure formation in non-Euclidean spaces of stimuli

image compression, data mining, and data visualization.
This is not unexpected, since these algorithms have also been successfully used in models that concern the development of biological
neural systems responsible for image processing in animals.
The working hypothesis is that the visual system is optimized for processing stimulation from the natural enviroment i.e. the manifold of natural images, which represent only a small fraction of all combinationally possible pixel patterns.
The region of interest of the present approach is visual cortex, area V1.
Results from numerical investigations are presented, that are intended to reproduce the early development of this part of the brain.
In contrast to previous approaches, these models take into account that in general the above mentioned manifold is non-Euclidean.
The non-Euclidean approach yields an improved reproduction of topological phenomena that are found in the biological counterpart.
The results are discussed and compared with results from alternative explanations.