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methodology-11

Low-Rank Matrix Completion

3260 papers • 126 benchmarks • 313 datasets

Low-Rank Matrix Completion is an important problem with several applications in areas such as recommendation systems, sketching, and quantum tomography. The goal in matrix completion is to recover a low rank matrix, given a small number of entries of the matrix. Source: Universal Matrix Completion

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Most implemented papers

Collaborative Filtering with Graph Information: Consistency and Scalable Methods

Hsiang-Fu Yu, I. Dhillon, Nikhil S. Rao, Pradeep Ravikumar•Sun Dec 06 2015

This work formulate and derive a highly efficient, conjugate gradient based alternating minimization scheme that solves optimizations with over 55 million observations up to 2 orders of magnitude faster than state-of-the-art (stochastic) gradient-descent based methods.

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Guaranteed Rank Minimization via Singular Value Projection

I. Dhillon, Prateek Jain, Raghu Meka•Tue Sep 29 2009

Results show that the SVP-Newton method is significantly robust to noise and performs impressively on a more realistic power-law sampling scheme for the matrix completion problem.

572 0

A Gradient Descent Algorithm on the Grassman Manifold for Matrix Completion

Raghunandan H. Keshavan, Sewoong Oh•Mon Oct 26 2009

A tensor pattern which is an extension of matrix is introduced into modeling the traffic data for the first time, which can give full play to traffic spatial–temporal information and preserve the multi-way nature of traffic data.

404 0

Orthogonal Rank-One Matrix Pursuit for Low Rank Matrix Completion

Jieping Ye, Z. Wang, M. Lai, Zhaosong Lu, Wei Fan, H. Davulcu•Thu Apr 03 2014

An efficient and scalable low rank matrix completion algorithm to extend the orthogonal matching pursuit method from the vector case to the matrix case is proposed and an economic version is proposed by introducing a novel weight updating rule to reduce the time and storage complexity.

100 0

Distant Supervision for Relation Extraction with Matrix Completion

Qiang Zhou, Zhiyuan Liu, M. Fan, T. Zheng, Deli Zhao, Edward Y. Chang•Sat May 31 2014

Experiments on two widely used datasets with different dimensions of textual features demonstrate that the low-rank matrix completion approach significantly outperforms the baseline and the state-of-the-art methods.

64 0

Depth Image Inpainting: Improving Low Rank Matrix Completion With Low Gradient Regularization

Deng Cai, Hongyang Xue, Shengming Zhang•Tue Apr 19 2016

A low gradient regularization method is proposed in which the penalty for small gradients is reduced while penalizing the nonzero gradients to allow for gradual depth changes.

121 0

Riemannian stochastic variance reduced gradient on Grassmann manifold

Bamdev Mishra, Hiroyuki Kasai, Hiroyuki Sato•Mon May 23 2016

This paper proposes a novel Riemannian extension of the Euclidean stochastic variance reduced gradient algorithm (R-SVRG) to a compact manifold search space and shows the developments on the Grassmann manifold.

22 0

Algebraic Variety Models for High-Rank Matrix Completion

Greg Ongie, R. Willett, R. Nowak, L. Balzano•Mon Mar 27 2017

This work considers a generalization of low-rank matrix completion to the case where the data belongs to an algebraic variety, i.e. each data point is a solution to a system of polynomial equations, and proposes an efficient matrix completion algorithm that minimizes a convex or non-convex surrogate of the rank of the matrix of monomial features.

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Low-Rank Matrix Completion | State-of-the-Art