Random Projection and Its Application to Learning

Random projection is a technique of mapping a number of points in a high-dimensional space into a low dimensional space with the property that the Euclidean distance of any two points is approximately pre-served through the projection. A random projection from Rn to Rk is typically defined as a random n×k matrix R = (rij) with each entry chosen randomly and independently according to some probability distri-bution: an n-dimensional vector u ∈ Rn is projected to u ′ = 1√