Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/fundamental-conditions-on-the-sampling-pattern-for-union-of-low-rank-ZCnDrkpQT8
References (43)
-
Daniel Pimentel-Alarcón, R. Nowak (2016)
The Information-Theoretic Requirements of Subspace Clustering with Missing Data -
Xiao-Yang Liu, S. Aeron, V. Aggarwal, Xiaodong Wang (2016)
Low-Tubal-Rank Tensor Completion Using Alternating MinimizationIEEE Transactions on Information Theory, 66
-
L. Eldén (2007)
Matrix methods in data mining and pattern recognition, 4
-
Lance Parsons, E. Haque, Huan Liu (2004)
Subspace clustering for high dimensional data: a reviewSIGKDD Explor., 6
-
Wenqi Wang, V. Aggarwal, S. Aeron (2016)
Tensor Completion by Alternating Minimization under the Tensor Train (TT) ModelArXiv, abs/1609.05587
-
Jian-Feng Cai, E. Candès, Zuowei Shen (2008)
A Singular Value Thresholding Algorithm for Matrix CompletionSIAM J. Optim., 20
-
Dinesh Manocha (2002)
SOLVING SYSTEMS OF POLYNOMIAL EQUATIONS, 97
-
Morteza Ashraphijuo, Ramtin Madani, J. Lavaei (2016)
Characterization of rank-constrained feasibility problems via a finite number of convex programs2016 IEEE 55th Conference on Decision and Control (CDC)
-
Morteza Ashraphijuo, Xiaodong Wang (2017)
Fundamental Conditions for Low-CP-Rank Tensor CompletionArXiv, abs/1703.10740
-
A. Krishnamurthy, Aarti Singh (2013)
Low-Rank Matrix and Tensor Completion via Adaptive Sampling -
Brian Eriksson, L. Balzano, R. Nowak (2012)
High-Rank Matrix Completion -
Morteza Ashraphijuo, Xiaodong Wang, Junwei Zhang (2019)
Low-Rank Data Completion With Very Low Sampling Rate Using Newton's MethodIEEE Transactions on Signal Processing, 67
-
E. Candès, T. Tao (2009)
The Power of Convex Relaxation: Near-Optimal Matrix CompletionIEEE Transactions on Information Theory, 56
-
D. Goldfarb, Zhiwei Qin (2013)
Robust Low-Rank Tensor Recovery: Models and AlgorithmsSIAM J. Matrix Anal. Appl., 35
-
Daniel Pimentel-Alarcón, R. Nowak, L. Balzano (2014)
On the sample complexity of subspace clustering with missing data2014 IEEE Workshop on Statistical Signal Processing (SSP)
-
Pengzhi Gao, Meng Wang, J. Chow, M. Berger, Lee Seversky (2017)
Missing Data Recovery for High-Dimensional Signals With Nonlinear Low-Dimensional StructuresIEEE Transactions on Signal Processing, 65
-
N. Kreimer, A. Stanton, M. Sacchi (2013)
Tensor completion based on nuclear norm minimization for 5D seismic data reconstructionGeophysics, 78
-
Xiao-Yang Liu, S. Aeron, V. Aggarwal, Xiaodong Wang, Minyou Wu (2015)
Adaptive Sampling of RF Fingerprints for Fine-Grained Indoor LocalizationIEEE Transactions on Mobile Computing, 15
-
Pengzhi Gao, Ren Wang, Meng Wang, J. Chow (2016)
Low-rank matrix recovery from quantized and erroneous measurements: Accuracy-preserved data privatization in power grids2016 50th Asilomar Conference on Signals, Systems and Computers
-
Hui Ji, Chaoqiang Liu, Zuowei Shen, Yuhong Xu (2010)
Robust video denoising using low rank matrix completion2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition
-
L Parsons, E Haque, H Liu (2004)
Subspace clustering for high dimensional data: A reviewACM SIGKDD Explor. Newslett., 6
-
Pengzhi Gao, Meng Wang, Scott Ghiocel, J. Chow, B. Fardanesh, G. Stefopoulos (2016)
Missing Data Recovery by Exploiting Low-Dimensionality in Power System Synchrophasor MeasurementsIEEE Transactions on Power Systems, 31
-
Morteza Ashraphijuo, V. Aggarwal, Xiaodong Wang (2016)
Deterministic and Probabilistic Conditions for Finite Completability of Low-Tucker-Rank TensorIEEE Transactions on Information Theory, 65
-
Nicholas Harvey, David Karger, K. Murota (2005)
Deterministic network coding by matrix completion -
Morteza Ashraphijuo, Xiaodong Wang (2018)
A Characterization of Sampling Patterns for Union of Low-Rank Subspaces Retrieval Problem -
Marco Signoretto, D. Tran, L. Lathauwer, J. Suykens (2014)
Learning with tensors: a framework based on convex optimization and spectral regularizationMachine Learning, 94
-
Brian Eriksson, L. Balzano, R. Nowak (2011)
High-Rank Matrix Completion and Subspace Clustering with Missing DataArXiv, abs/1112.5629
-
Morteza Ashraphijuo, V. Aggarwal, Xiaodong Wang (2017)
On Deterministic Sampling Patterns for Robust Low-Rank Matrix CompletionIEEE Signal Processing Letters, 25
-
Morteza Ashraphijuo, Xiaodong Wang, V. Aggarwal (2017)
Rank Determination for Low-Rank Data CompletionJ. Mach. Learn. Res., 18
-
Daniel Pimentel-Alarcón, N. Boston, R. Nowak (2015)
A characterization of deterministic sampling patterns for low-rank matrix completion2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton)
-
D. Kressner, M. Steinlechner, Bart Vandereycken (2014)
Low-rank tensor completion by Riemannian optimizationBIT Numerical Mathematics, 54
-
Bernardino Romera-Paredes, M. Pontil (2013)
A New Convex Relaxation for Tensor CompletionArXiv, abs/1307.4653
-
Daniel Pimentel-Alarcón, L. Balzano, R. Nowak (2016)
Necessary and sufficient conditions for sketched subspace clustering2016 54th Annual Allerton Conference on Communication, Control, and Computing (Allerton)
-
E. Candès, B. Recht (2008)
Exact Matrix Completion via Convex OptimizationFoundations of Computational Mathematics, 9
-
Ryota Tomioka, K. Hayashi, H. Kashima (2010)
Estimation of low-rank tensors via convex optimizationarXiv: Machine Learning
-
Daniel Pimentel-Alarcón, N. Boston, R. Nowak (2014)
Deterministic conditions for subspace identifiability from incomplete sampling2015 IEEE International Symposium on Information Theory (ISIT)
-
Daniel Pimentel-Alarcón, L. Balzano, Roummel Marcia, R. Nowak, R. Willett (2016)
Group-sparse subspace clustering with missing data2016 IEEE Statistical Signal Processing Workshop (SSP)
-
Morteza Ashraphijuo, Xiaodong Wang (2019)
Clustering a union of low-rank subspaces of different dimensions with missing dataPattern Recognit. Lett., 120
-
Morteza Ashraphijuo, Xiaodong Wang, V. Aggarwal (2017)
Deterministic and Probabilistic Conditions for Finite Completability of Low-rank Multi-View DataArXiv, abs/1701.00737
-
E. Candès, Yonina Eldar, T. Strohmer, V. Voroninski (2011)
Phase Retrieval via Matrix CompletionSIAM J. Imaging Sci., 6
-
D. Calvetti (2009)
Matrix methods in data mining and pattern recognitionMath. Comput., 78
-
Silvia Gandy, B. Recht, I. Yamada (2011)
Tensor completion and low-n-rank tensor recovery via convex optimizationInverse Problems, 27
-
Ehsan Elhamifar, René Vidal (2009)
Sparse subspace clustering2009 IEEE Conference on Computer Vision and Pattern Recognition
- Publisher
- Springer Journals
- Copyright
- Copyright © 2019 by Springer Nature Switzerland AG
- Subject
- Computer Science; Artificial Intelligence; Mathematics, general; Computer Science, general; Complex Systems
- ISSN
- 1012-2443
- eISSN
- 1573-7470
- DOI
- 10.1007/s10472-019-09662-6
- Publisher site
- See Article on Publisher Site
Abstract
This paper is concerned with investigating the fundamental conditions on the locations of the sampled entries, i.e., sampling pattern, for finite completability of a matrix that represents the union of several subspaces with given ranks. In contrast with the existing analysis on Grassmannian manifold for the conventional matrix completion, we propose a geometric analysis on the manifold structure for the union of several subspaces to incorporate all given rank constraints simultaneously. In order to obtain the deterministic conditions on the sampling pattern, we characterizes the algebraic independence of a set of polynomials defined based on the sampling pattern, which is closely related to finite completion. We also give a probabilistic condition in terms of the number of samples per column, i.e., the sampling probability, which leads to finite completability with high probability. Furthermore, using the proposed geometric analysis for finite completability, we characterize sufficient conditions on the sampling pattern that ensure there exists only one completion for the sampled data.
Journal
Annals of Mathematics and Artificial Intelligence – Springer Journals
Published: Aug 16, 2019