Random Projection

Sun, 10 Jan 2016 02:13:13 +0000

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.

Dimensionality Reduction on Infinite Script

Random Projection

Introduction