The curse of dimensionality

Half of the points sampled uniformly distibuted at radom in an area of w × h will be located at the edges of this 2-D region.

area( ) = area( ) =

2-D slice of a 3-D volume

The higher the dimension of the sampling space, the more points are on the edges relative to the amounts of points sampled.

volume( ) = volume( ) =

2-D slice of a 4-D hypervolume

hypervolume( ) = hypervolume( ) =