It has to a lot to do with statistics, but is not usually classified as statistics per-se, but I think the entire field that includes Random Projections (e.g. Johanson-Lindenstrauss Lemma), Compressive Sensing and friends.

Statistically speaking, it says that regardless of the dimension that data is presented in, a random linear projection to (slightly more than) the intrinsic dimension of the data captures the underlying topology.