Near optimal column-based matrix reconstruction
Christos Boutsidis, Petros Drineas, et al.
FOCS 2011
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.
Christos Boutsidis, Petros Drineas, et al.
FOCS 2011
Elizabeth Newman, Lior Horesh, et al.
Frontiers in Big Data
Haim Avron, Vikas Sindhwani, et al.
NeurIPS 2013
Insu Han, Dmitry Malioutov, et al.
SIAM Journal on Scientific Computing