Topic: Matrix sketching

Building on the preceding linear-algebra tutorials, this lecture presents two further approaches to matrix sketching: leverage-score sampling and the Subsampled Randomized Hadamard Transform. It examines how these methods produce effective compressed matrix representations for a variety of applications.

Randomization offers an alternative approach to large matrix computations arising in scientific data analysis. This talk explains how randomized algorithms approximate matrix multiplication and singular-value decomposition, solve least-squares problems and linear systems, and support data-analysis applications. The accompanying presentation develops matrix sketches through row and column sampling, compares length-squared sampling with leverage-score sampling, and describes their use in low-rank approximation and matrix factorizations. It also explains how leverage scores can be approximated ef