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10 years 5 months ago
Low-rank matrix completion with geometric performance guarantees
—The low-rank matrix completion problem can be stated as follows: given a subset of the entries of a matrix, find a low-rank matrix consistent with the observations. There exist...
Wei Dai, Ely Kerman, Olgica Milenkovic
130views Education» more  TIT 2010»
10 years 8 months ago
The power of convex relaxation: near-optimal matrix completion
This paper is concerned with the problem of recovering an unknown matrix from a small fraction of its entries. This is known as the matrix completion problem, and comes up in a gr...
Emmanuel J. Candès, Terence Tao
170views more  SIAMREV 2010»
10 years 8 months ago
Network Properties Revealed through Matrix Functions
The newly emerging field of Network Science deals with the tasks of modelling, comparing and summarizing large data sets that describe complex interactions. Because pairwise affin...
Ernesto Estrada, Desmond J. Higham
164views more  SIAMMAX 2010»
10 years 8 months ago
Uniqueness of Low-Rank Matrix Completion by Rigidity Theory
The problem of completing a low-rank matrix from a subset of its entries is often encountered in the analysis of incomplete data sets exhibiting an underlying factor model with app...
Amit Singer, Mihai Cucuringu
172views more  SIAMCOMP 2010»
10 years 8 months ago
Deterministic Polynomial Time Algorithms for Matrix Completion Problems
We present new deterministic algorithms for several cases of the maximum rank matrix completion problem (for short matrix completion), i.e. the problem of assigning values to the ...
Gábor Ivanyos, Marek Karpinski, Nitin Saxen...
147views more  JMLR 2010»
10 years 8 months ago
Spectral Regularization Algorithms for Learning Large Incomplete Matrices
We use convex relaxation techniques to provide a sequence of regularized low-rank solutions for large-scale matrix completion problems. Using the nuclear norm as a regularizer, we...
Rahul Mazumder, Trevor Hastie, Robert Tibshirani
10 years 8 months ago
Dynamic normal forms and dynamic characteristic polynomial
Abstract. We present the first fully dynamic algorithm for computing the characteristic polynomial of a matrix. In the generic symmetric case our algorithm supports rank-one updat...
Gudmund Skovbjerg Frandsen, Piotr Sankowski
177views more  SIAMSC 2011»
10 years 8 months ago
Computing f(A)b via Least Squares Polynomial Approximations
Given a certain function f, various methods have been proposed in the past for addressing the important problem of computing the matrix-vector product f(A)b without explicitly comp...
Jie Chen, Mihai Anitescu, Yousef Saad
10 years 8 months ago
Recovering Low-Rank and Sparse Components of Matrices from Incomplete and Noisy Observations
Many applications arising in a variety of fields can be well illustrated by the task of recovering the low-rank and sparse components of a given matrix. Recently, it is discovered...
Min Tao, Xiaoming Yuan