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Matrix Recovery with Implicitly Low-Rank Data [article]

Xingyu Xie, Jianlong Wu, Guangcan Liu, Jun Wang
2018 arXiv   pre-print
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

Dehui Yang, Michael B. Wakin
2015 2015 International Conference on Sampling Theory and Applications (SampTA)  
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

Nauman Shahid, Vassilis Kalofolias, Xavier Bresson, Michael Bronstein, Pierre Vandergheynst
2015 2015 IEEE International Conference on Computer Vision (ICCV)  
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

Juan Andres Bazerque, Gonzalo Mateos, Georgios B. Giannakis
2013 2013 IEEE International Conference on Acoustics, Speech and Signal Processing  
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]

Greg Ongie, Mathews Jacob
2017 arXiv   pre-print
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]

Guangcan Liu, Ju Sun, Shuicheng Yan
2010 arXiv   pre-print
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]

Jicong Fan, Yuqian Zhang, Madeleine Udell
2019 arXiv   pre-print
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

Jicong Fan, Yuqian Zhang, Madeleine Udell
2020 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
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

Gregory Ongie, Mathews Jacob
2017 IEEE Transactions on Computational Imaging  
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

Sebastian Ohse, Melanie Boerries, Hauke Busch
2019 PeerJ Computer Science  
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]

Nauman Shahid, Nathanael Perraudin, Pierre Vandergheynst
2016 arXiv   pre-print
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

Zhao Zhang, Shuicheng Yan, Mingbo Zhao, Fan-Zhang Li
2015 Knowledge-Based Systems  
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

Jicong Fan, Madeleine Udell
2019 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)  
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

Zhonghu Xu, Linjun Zhang, Jinqi Shen, Hao Zhou, Xuefeng Liu, Jiannong Cao, Kai Xing
2019 EURASIP Journal on Wireless Communications and Networking  
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

Shiyu Zhai, Guobing Li, Guomei Zhang, Zefeng Qi
2021 IET Signal Processing  
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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