Distances between samples in high dimensions. Curse of dimensions?

Gerenuk

Hello,

I remember that I heard something about the curse of dimensions when discrimitating between samples with high dimensional parameters. Therefore a sample might have the property vector (x1,x2,...,xn) and one could define a measure of distance (euclidean, manhattan, ...) to judge how close two samples are in their qualities.

The problem that arises in high dimension is, that effectively all random samples will have a very similar distance between a pair! Somehow that was also obvious from looking at volume of high dimensional cube and spheres.

Does anyone know good references to read up about this problem or does anyone know about solutions to this dilemma?