Low-rank matrix approximations, such as the truncated singular value decomposition and
the rank-revealing QR decomposition, play a central role in data analysis and scientific …

RandNLA: randomized numerical linear algebra Page 1 80 COMMUNICATIONS OF THE ACM
| JUNE 2016 | VOL. 59 | NO. 6 review articles DOI:10.1145/2842602 Randomization offers new …

This survey highlights the recent advances in algorithms for numerical linear algebra that
have come from the technique of linear sketching, whereby given a matrix, one first …

This tutorial text gives a unifying perspective on machine learning by covering both
probabilistic and deterministic approaches-which are based on optimization techniques …

We design a new distribution over m× n matrices S so that, for any fixed n× d matrix A of rank
r, with probability at least 9/10,∥ SAx∥ 2=(1±ε)∥ Ax∥ 2 simultaneously for all x∈ R d …

For massive data, the family of subsampling algorithms is popular to downsize the data
volume and reduce computational burden. Existing studies focus on approximating the …

Randomized algorithms for very large matrix problems have received a great deal of
attention in recent years. Much of this work was motivated by problems in large-scale data …

One approach to improving the running time of kernel-based methods is to build a small
sketch of the kernel matrix and use it in lieu of the full matrix in the machine learning task of …

Excerpt More than 25 years have passed since the first edition of this book was published in
1996. Least squares and least-norm problems have become more significant with every …

Extraordinary amounts of data are being produced in many branches of science. Proven
statistical methods are no longer applicable with extraordinary large datasets due to …