Haim Avron, Anshul Gupta
SC 2012
We study the following problem of subset selection for matrices: given a matrix X ε ℝnxm (m > n) and a sampling parameter k (n ≤ k ≤ m), select a subset of k columns from X such that the pseudoinverse of the sampled matrix has as small a norm as possible. In this work, we focus on the Frobenius and the spectral matrix norms. We describe several novel (deterministic and randomized) approximation algorithms for this problem with approximation bounds that are optimal up to constant factors. Additionally, we show that the combinatorial problem of finding a low-stretch spanning tree in an undirected graph corresponds to subset selection, and discuss various implications of this reduction. © by SIAM.
Haim Avron, Anshul Gupta
SC 2012
Haim Avron, Andrei Sharf, et al.
ACM Transactions on Graphics
Gal Shulkind, Lior Horesh, et al.
SIAM/ASA JUQ
Christos Boutsidis, Petros Drineas, et al.
NeurIPS 2011