Data Mining - High Dimension (Curse of Dimensionality)

Thomas Bayes


High dimension

In high dimension, it's really difficult to stay local.

In high dimensions, all cases are edge cases

Sam Ross


See this interactive app in R Shiny on the wiki/Curse of Dimensionality.

Circle example: The circle fills up most of the area in the square, in fact it takes up exactly <math>\pi</math> out of 4 which is about 78%. In three dimensions we have a sphere and a cube, and the ratio of sphere volume to cube volume is a bit smaller, <math>\frac{4\pi}{3}</math> out of a total of 8, which is just over 52%

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