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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Low Rank Matrix Recovery for Seismic Data Analysis and Blind Superresolution
地震数据分析 盲超分辨率 低秩 矩阵恢复
2023/2/27
Low rank matrix recovery is about reconstructing a low rank matrix from incomplete measurements. It arises frequently in many research areas of science and engineering, for example, machine learning, ...
Tight Oracle Bounds for Low-rank Matrix Recovery from a Minimal Number of Random Measurements
Matrix completion The Dantzig selector oracle inequalities norm of random matrices convex optimization and semidefinite programming
2015/6/17
This paper presents several novel theoretical results regarding the recovery of a low-rank matrix from just a few measurements consisting of linear combinations of the matrix entries. We show that pro...
Randomized Algorithms for Low-Rank Matrix Factorizations:Sharp Performance Bounds
Randomized Algorithms Low-Rank Matrix Factorizations Sharp Performance Bounds
2015/6/17
The development of randomized algorithms for numerical linear algebra, e.g. for computing approximate QR and SVD factorizations, has recently become an intense area of research. This paper studies one...
Realizability of Polytopes as a Low Rank Matrix Completion Problem
Realizability of Polytopes Low Rank Matrix Completion Problem
2010/12/31
Here we show that the problem of realizing a polytope with specified combinatorics is equivalent to a low rank matrix completion problem.This is comparable to known results reducing realizability to s...
Low-Rank Matrix Approximation with Weights or Missing Data is NP-hard
low-rank matrix approximation weighted low-rank approximation missing data
2010/12/31
Weighted low-rank approximation (WLRA), a dimensionality reduction technique for data anal-
ysis, has been successfully used in several applications, such as in collaborative filtering to design reco...
Von Neumann Entropy Penalization and Low Rank Matrix Estimation
low rank matrix estimation von Neumann entropy
2010/9/14
A problem of estimation of a Hermitian nonnegatively definite matrix ρ of unit trace (for instance, a density matrix of a quantum system) based on n independent measurements
Yj = tr(ρXj) + ξj , j = 1...