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Random Projection

Introduction In mathematics and statistics, random projection is a technique used to reduce the dimensionality of a set of points which lie in Euclidean space. Random projection methods are known for their simplicity and low error rates compared with other dimensionality-reduction techniques, and experiments show that they preserve pairwise distances well. Consider a problem as follows: We have a set of $n$ points in a high-dimensional Euclidean space $\mathbf{R}^d$. We want to project the points onto a space of low dimension $\mathbf{R}^k$ in such a way that pairwise distances of the points are approximately the same as before.