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Paradoxical Behavior of Multidimensional Data

version 1.0.0.0 (97.5 KB) by Ilias Konsoulas
Three counter-intuitive examples of how data behave in Multidimensional Euclidean Space.

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Updated 28 Sep 2015

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This submission provides three examples of at least paradoxical phenomena that happen in higher dimensions:
Example A proves that the greatest volume part of a hypercube is concentrated at its corners.
Example B proves that virtually all of the content of a hypersphere is concentrated close to its surface.
Finally, Example C also proves that the probability mass of a multivariate Normal distribution exhibits a rapid
migration into the extreme tails. In very high dimensions, virtually the entire sample will be in the distribution tails!
The theory of these examples was reproduced from the book:
"Multivariate Density Estimation - Theory, Practice, and Visualization" by David W. Scott, 1992, John Wiley & Sons, Inc.
I confirmed the theoretical formulas by use of Monte Carlo simulations because originally I had trouble to believe them!

Cite As

Ilias Konsoulas (2021). Paradoxical Behavior of Multidimensional Data (https://www.mathworks.com/matlabcentral/fileexchange/53260-paradoxical-behavior-of-multidimensional-data), MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R2011b
Compatible with any release
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