# Data Mining - High Dimension (Curse of Dimensionality)

High dimension

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

In high dimensions, all cases are edge cases Sam Ross

## 3 - Example

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

Circle example: The circle fills up most of the area in the square, in fact it takes up exactly $\pi$ 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, $\frac{4\pi}{3}$ out of a total of 8, which is just over 52%