Sketching for Geometric Problems

In this invited talk at the European Symposium on Algorithms (ESA), 2017, I will discuss a tool called sketching, which is a form of data dimensionality reduction, and its applications to several problems in high dimensional geometry. In particular, I will show how to obtain the fastest possible algorithms for fundamental problems such as projection onto a flat, and also study generalizations of projection onto more complicated objects such as the union of flats or subspaces. Some of these problems are just least squares regression problems, with many applications in machine learning, numerical linear algebra, and optimization. I will also discuss low rank approximation, with applications to clustering. Finally I will mention a number of other applications of sketching in machine learning, numerical linear algebra, and optimization. 1998 ACM Subject Classification F.2 Analysis of Algorithms and Problem Complexity