test

testrembed.m

This file exhibits the basic guarantee of the randomized embedding code.

Given features X and labels Y, where the SVD of X is given by

X = U_X Σ_X V_X

and the SVD of (U_X^T Y) is

U_X^T Y = U_E Σ_E V_E,

the k-dimensional embedding is defined as the first k columns of V_E. This definition is motivated by the optimal rank-constrained least-squares approximation of Y given X, as explained in this paper.

Randomized methods provide a fast way of approximating these SVDs when the dimensionalities are large.