TTIC / CMSC 31150 Mathematical Toolkit Spring 2013 Lecture 1 : April 24 , 2013

In this lecture we talk about various useful applications of dimensionality reduction, specifically using JohnsonLindenstrauss lemma. JL lemma states that a small set of points in a high-dimensional space can be embedded into a space of much lower dimension in such a way that distances between the points are nearly preserved. In the previous lecture, we looked at one such linear embedding whose entries were sampled from iid Gaussian distribution. We look at the applications of dimensionality reduction in Singular value decomposition. And we will use the techniques of random projections in finding approximate solution to the graph-coloring problem.