An information geometrical evaluation of Shannon information metrics on a discrete n-dimensional digital manifold
Abstract
The definition and nature of information have perplexed scientists due to its dual nature in measurements. The information is discrete and continuous when evaluated on a metric scale and the Laplace-Beltrami operator and Gauss-Bonnet Theorem can map one to another. On the other hand defining the information as a discrete entity on the surface area of an n-dimensional discrete digital manifold provides a unique way of calculating the entropy of a manifold. The software simulation shows that the surface area of the discrete n-dimensional digital manifold is an effectively computable function. Moreover it also provides the information-geometrical evaluation of Shannon information metrics.
URI
http://dx.doi.org/10.1016/j.heliyon.2023.e16653https://dspace.yasar.edu.tr/handle/20.500.12742/19243
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