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What are Random Projection Trees?
Random Projection Trees is a recursive space partitioning datastructure which can automatically adapt to the underlying (linear or non-linear) structure in data. It has strong theoretical guarantees on rates of convergence and works well in practice.

You can use RPTrees to learn the structure of manifolds, perform fast nearest-neighbor searches, do vector-quantization of the underlying density, and much more.

RPTree Tutorials:
You can start using RPTrees by following the tutorials.

Technical Papers:
RPTrees with applications to manifold learning was presented in NIPS 2007:
Learning the structure of manifolds using random projections.

A rigourous theoretical analysis of the technique was done shortly before in the UCSD Technical Report 2007:
Random projection trees and low dimensional manifolds.