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Matrix Recovery with Implicitly Low-Rank Data
[article]
2018
arXiv
pre-print
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To tackle this issue, we propose a novel method for matrix recovery in this paper, which could well handle the case where the target matrix is low-rank in an implicit feature space but high-rank or even ...
However, the underlying data structure is often non-linear in practice, therefore the low-rankness assumption could be violated. ...
In general, KPCA could apply to the data matrix that is implicitly low-rank but originally high-rank. ...
arXiv:1811.03945v1
fatcat:unxcilrdfna4ng6o6oz2dr3ssy
Modeling and recovering non-transitive pairwise comparison matrices
2015
2015 International Conference on Sampling Theory and Applications (SampTA)
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implicitly: aggregating voter rankings, ratings databases, etc. explicitly: direct surveys, polling, competitions, etc. • Data may be noisy, incomplete. ...
The closest transitive matrix is generated using the score vector
Example Recovery Result • Suppose s 1 , s 2 , …, s r , a 1 , a 2 , …, a r are orthonormal with coherence μ, and that Then with random ...
doi:10.1109/sampta.2015.7148846
fatcat:k2o2uycjbzbsxjuaf2hjceef5e
Robust Principal Component Analysis on Graphs
2015
2015 IEEE International Conference on Computer Vision (ICCV)
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on the low-rank matrix, and 4) convexity of the resulting optimization problem. ...
Extensive experiments on 8 benchmark, 3 video and 2 artificial datasets with corruptions clearly reveal that our model outperforms 10 other state-of-the-art models in its clustering and low-rank recovery ...
Exact low-rank recovery: Unlike factorized models we target the exact low-rank recovery by modeling the data matrix as the sum of low-rank L and a sparse matrix S. ...
doi:10.1109/iccv.2015.322
dblp:conf/iccv/ShahidKBBV15
fatcat:eqlcu25movct7p7zccrax4hjtm
Inference of Poisson count processes using low-rank tensor data
2013
2013 IEEE International Conference on Acoustics, Speech and Signal Processing
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A novel regularizer capturing the tensor rank is introduced in this paper as the key enabler for completion of three-way data arrays with missing entries. ...
Tests on simulated and real datasets corroborate the sparsifying regularization effect, and demonstrate recovery of 15% missing RNA-sequencing data with an inference error of −12dB. ...
Low rank is an attribute capturing this regularity that can be readily exploited when data are organized into a matrix. ...
doi:10.1109/icassp.2013.6638814
dblp:conf/icassp/BazerqueMG13
fatcat:ymsmrccp3zaivi65zytqhqfevy
A Fast Algorithm for Convolutional Structured Low-Rank Matrix Recovery
[article]
2017
arXiv
pre-print
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Fourier domain structured low-rank matrix priors are emerging as powerful alternatives to traditional image recovery methods such as total variation and wavelet regularization. ...
These priors specify that a convolutional structured matrix, i.e., Toeplitz, Hankel, or their multi-level generalizations, built from Fourier data of the image should be low-rank. ...
SIGNAL RECONSTRUCTION BY CONVOLUTIONAL STRUCTURED LOW-RANK MATRIX RECOVERY A. ...
arXiv:1609.07429v3
fatcat:pvn62si76rh2ldxz3y4phvk7k4
Closed-Form Solutions to A Category of Nuclear Norm Minimization Problems
[article]
2010
arXiv
pre-print
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It is an efficient and effective strategy to utilize the nuclear norm approximation to learn low-rank matrices, which arise frequently in machine learning and computer vision. ...
In this paper we shall prove that the following Low-Rank Representation (LRR) icml_2010_lrr,lrr_extention problem: eqnarray*_ZZ_*, & s.t., & X=AZ, eqnarray* has a unique and closed-form solution, where ...
X = D + E. (1) The minimizer D * (with respect to the variable D) gives a low-rank recovery to the original data X 0 . ...
arXiv:1011.4829v2
fatcat:kslmztrpgfe3ph33prqf5qsxny
Polynomial Matrix Completion for Missing Data Imputation and Transductive Learning
[article]
2019
arXiv
pre-print
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This paper develops new methods to recover the missing entries of a high-rank or even full-rank matrix when the intrinsic dimension of the data is low compared to the ambient dimension. ...
Comparative studies on synthetic data, subspace clustering with missing data, motion capture data recovery, and transductive learning verify the superiority of our methods over the state-of-the-art. ...
Introduction The low-rank matrix completion (LRMC) problem is to recover the missing entries of a partially observed matrix of low-rank (Candès and Recht 2009) . ...
arXiv:1912.06989v1
fatcat:3qq2oacg45ayfgiicqgubh2aim
Polynomial Matrix Completion for Missing Data Imputation and Transductive Learning
2020
PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE
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This paper develops new methods to recover the missing entries of a high-rank or even full-rank matrix when the intrinsic dimension of the data is low compared to the ambient dimension. ...
Comparative studies on synthetic data, subspace clustering with missing data, motion capture data recovery, and transductive learning verify the superiority of our methods over the state-of-the-art. ...
Introduction The low-rank matrix completion (LRMC) problem is to recover the missing entries of a partially observed matrix of low-rank (Candès and Recht 2009) . ...
doi:10.1609/aaai.v34i04.5796
fatcat:o6aixy5vmrgthninrr4vfbwe4q
A Fast Algorithm for Convolutional Structured Low-Rank Matrix Recovery
2017
IEEE Transactions on Computational Imaging
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Fourier domain structured low-rank matrix priors are emerging as powerful alternatives to traditional image recovery methods such as total variation (TV) and wavelet regularization. ...
These priors specify that a convolutional structured matrix, i.e., Toeplitz, Hankel, or their multi-level generalizations, built from Fourier data of the image should be low-rank. ...
Comparison of GIRAF with competing algorithms for structured low-rank matrix recovery with noisy data using a piecewise constant SLRA model. ...
doi:10.1109/tci.2017.2721819
pmid:29911129
pmcid:PMC5999344
fatcat:y3rmdw7qxbfwxcrm36kc6m3qpu
Blind normalization of public high-throughput databases
2019
PeerJ Computer Science
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Without such normalization, meta-analyses can be difficult to perform and the potential to address shortcomings in experimental designs, such as inadequate replicates or controls with public data, is limited ...
The inherent recovery of confounding factors is formulated in the theoretical framework of compressed sensing and employs efficient optimization on manifolds. ...
The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. ...
doi:10.7717/peerj-cs.231
pmid:33816884
pmcid:PMC7924423
fatcat:ynehinptqvbxrdwz6hzzlonop4
Low-Rank Matrices on Graphs: Generalized Recovery & Applications
[article]
2016
arXiv
pre-print
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Surprisingly, our analysis confirms that it is possible to recover many approximate linear and non-linear low-rank structures with recovery guarantees with a set of highly scalable and efficient algorithms ...
We revisit the problem of low-rank recovery from a totally different perspective, involving graphs which encode pairwise similarity between the data samples and features. ...
This model implicitly encodes the smoothness of the low-rank matrix X on the graph as tr(XLX ) = tr(V LV ), using X = U V . ...
arXiv:1605.05579v3
fatcat:q6iano5dwzbvxkupmuropiywda
Bilinear low-rank coding framework and extension for robust image recovery and feature representation
2015
Knowledge-Based Systems
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We mainly study the low-rank image recovery problem by proposing a bilinear low-rank coding framework called Tensor Low-Rank Representation. ...
with a clean informative dictionary via low-rank embedding. ...
LRR-PSD [45]
LRR with Positive Semi-Definite constraint
P; b
P
Embedding matrix
FLRR [43]
Fixed Low-Rank Representation
Y; b
Y
Low-rank recovery
TLRR
Tensor Low-Rank Representation
d ...
doi:10.1016/j.knosys.2015.06.001
fatcat:ggik3r5jafcqpjezziu3igd2ke
Online High Rank Matrix Completion
2019
2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)
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High rank matrix completion. Elhamifar [6] proposed to use group-sparse constraint to complete high rank matrix consisting of data drawn from union of low-dimensional subspaces. ...
Recent advances in matrix completion enable data imputation in full-rank matrices by exploiting low dimensional (nonlinear) latent structure. ...
Throughout this paper, we use the terms "low rank" or "high rank" matrix to mean a matrix whose rank is low or high relative to its side length. ...
doi:10.1109/cvpr.2019.00889
dblp:conf/cvpr/FanU19
fatcat:h2ih5rvjvvf55gr4i6szef7yvi
MRCS: matrix recovery-based communication-efficient compressive sampling on temporal-spatial data of dynamic-scale sparsity in large-scale environmental IoT networks
2019
EURASIP Journal on Wireless Communications and Networking
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Specifically, we exploit data correlation at both temporal and spatial domains, then provide a cross-domain basis to collect data and a low-rank matrix recovery design to recover the data. ...
data in a proper basis to compress effectively in order to reduce the magnitude of data to be collected, which implicitly assumes the sparsity of the data and inevitably may result in a poor data recovery ...
The data can be found at: https://github.com/oleotiger/experimental-data. ...
doi:10.1186/s13638-018-1312-1
fatcat:tm2gq7dlq5ej5ahu6fyd7oeka4
Spatio‐temporal signal recovery under diffusion‐induced smoothness and temporal correlation priors
2021
IET Signal Processing
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The authors then accordingly formulate a spatio-temporal signal recovery method by jointly exploiting the spatial smoothness, low rank and refined differential temporal smoothness. ...
The formulated recovery problem is solved by a block coordinate descent-based algorithm, which iteratively optimises the recovery accuracy and temporal correlation matrix. ...
Therefore, according to the signal model in Equation (7) , one can assume that the spatio-temporal signal is a low-rank matrix, with a rank equal to |F |. ...
doi:10.1049/sil2.12082
fatcat:cvkgat4vovanbcgjohjjqcdfpq
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