Fetching the paper…

Reading the bibliography…

2014

Matrix Completion and Low-Rank SVD via Fast Alternating Least Squares

Hastie, Trevor, Mazumder, Rahul, Lee, Jason et al.

Original
PDF
Post on X

Understand

The matrix-completion problem has attracted a lot of attention, largely as a result of the celebrated Netflix competition.

Two popular approaches for solving the problem are nuclear-norm-regularized matrix approximation (Candes and Tao, 2009, Mazumder, Hastie and Tibshirani, 2010), and maximum-margin matrix factorization (Srebro, Rennie and Jaakkola, 2005).
These two procedures are in some cases solving equivalent problems, but with quite different algorithms.
In this article we bring the two approaches together, leading to an efficient algorithm for large matrix factorization and completion that outperforms both of these.

Matrix Completion and Low-Rank SVD via Fast Alternating Least Squares · Around

Built on

Matrix Perturbation Theory
G. Stewart and Ji-Guang Sun · 1990
Earlier work this paper cites.
Derivatives of spectral functions
A. Lewis · 1996
Earlier work this paper cites.
Maximum margin matrix factorization
Nathan Srebro, Jason Rennie, and Tommi Jaakkola · 2005
Earlier work this paper cites.

Similar

The power of convex relaxation: Near-optimal matrix completion, 2009
Emmanuel J. Candès and Terence Tao · 2009
Cited alongside, same era.
Spectral regularization algorithms for learning large incomplete matrices
Rahul Mazumder, Trevor Hastie, and Rob Tibshirani · 2010
Cited alongside, same era.
Successive normalization of rectangular arrays
Richard Olshen and Bala Rajaratnam · 2010
Cited alongside, same era.

Then

Matrix computations , volume 3
Gene Golub and Charles Van Loan · 2012
Later among the works it cites.
softImpute: matrix completion via iterative soft-thresholded svd , 2013
Trevor Hastie and Rahul Mazumder · 2013
Later among the works it cites.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…