Paradoxical Behavior of Multidimensional Data

Three counter-intuitive examples of how data behave in Multidimensional Euclidean Space.
437 Downloads
Updated 28 Sep 2015

View License

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 (2024). 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
Platform Compatibility
Windows macOS Linux
Categories
Find more on Filter Banks in Help Center and MATLAB Answers

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!
Version Published Release Notes
1.0.0.0

I have corrected a couple of bugs in hypernormal.m.

Added a nice promo picture.