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Robust Recovery of Subspace Structures by Low-Rank Representation
2013
IEEE Transactions on Pattern Analysis and Machine Intelligence
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To this end, we propose a novel method termed Low-Rank Representation (LRR), which seeks the lowest-rank representation among all the candidates that can represent the data samples as linear combinations ...
It is shown that LRR well solves the subspace recovery problem: when the data is clean, we prove that LRR exactly captures the true subspace structures; for the data contaminated by outliers, we prove ...
To recover the subspace structures from the data containing errors, we propose a novel method termed low-rank representation (LRR) [14] . ...
doi:10.1109/tpami.2012.88
pmid:22487984
fatcat:azvd2z6lyjalxpghhhoxkrus5e
Learning Robust Data Representation: A Knowledge Flow Perspective
[article]
2020
arXiv
pre-print
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Along this line of research, low-rank modeling has been widely-applied to solving representation learning challenges. ...
This survey covers the topic from a knowledge flow perspective in terms of: (1) robust knowledge recovery, (2) robust knowledge transfer, and (3) robust knowledge fusion, centered around several major ...
First of all, robust subspace learning attempts to jointly seek an effective low-dimensional projection P by recovering the intrinsic structure of the noisy data with low-rank constraint [Li and Fu, 2016 ...
arXiv:1909.13123v2
fatcat:wll23rkrznejvhzsihc6rwcwve
Constrained Low-Rank Learning Using Least Squares-Based Regularization
2017
IEEE Transactions on Cybernetics
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2016 pre-print arXiv:1611.04870v1 fatcat:52qoz7mlkbcvnc6662iorkc6l4
Naturally, the data label structure tends to resemble that of the corresponding low-dimensional representation, which is derived from the robust subspace projection of clean data by low-rank learning. ...
This paper aims to learn both the discriminant low-rank representation (LRR) and the robust projecting subspace in a supervised manner. ...
[2] put forward Low-Rank Representation (LRR) which was proved to be very effective for robust subspace segmentation. ...
doi:10.1109/tcyb.2016.2623638
pmid:27849552
fatcat:znrgzbzxu5g5pmdcyeb3rmgkgq
Symmetric low-rank representation for subspace clustering
2016
Neurocomputing
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In particular, the SLRR method considers a collaborative representation combined with low-rank matrix recovery techniques as a low-rank representation to learn a symmetric low-rank representation, which ...
preserves the subspace structures of high-dimensional data. ...
The symmetric low-rank representation given by SLRR effectively preserves the subspace structures of high-dimensional data. ...
doi:10.1016/j.neucom.2015.08.077
fatcat:7mbbyp2jp5ag5fxvqo3p5ezene
Low-Rank Representation for Incomplete Data
2014
Mathematical Problems in Engineering
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As a significant component of LRMR, the model of low-rank representation (LRR) seeks the lowest-rank representation among all samples and it is robust for recovering subspace structures. ...
Firstly, we construct a nonconvex minimization by taking the low rankness, robustness, and incompletion into consideration. ...
Acknowledgments This work is partially supported by the National Natural ...
doi:10.1155/2014/439417
fatcat:3jp53soycbhhlnudcfd4yhnmuy
Exploiting low-dimensional structures to enhance DNN based acoustic modeling in speech recognition
2016
2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
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Relying on the fact that the intrinsic dimensions of the posterior subspaces are indeed very small and the matrix of all posteriors belonging to a class has a very low rank, we demonstrate how low-dimensional ...
We propose to model the acoustic space of deep neural network (DNN) class-conditional posterior probabilities as a union of low-dimensional subspaces. ...
Exploiting this multi low-rank structure of speech can lead to posterior enhancement via low-rank representation at utterance level [29] . ...
doi:10.1109/icassp.2016.7472767
dblp:conf/icassp/DigheLAB16
fatcat:jezw6rilvzf35fen5drjrxpe34
Online Low-Rank Representation Learning for Joint Multi-Subspace Recovery and Clustering
2018
IEEE Transactions on Image Processing
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In the second stage, the intrinsic principal components of the entire data set are computed incrementally by utilizing the learned subspace structure, and the low-rank representation matrix can also be ...
In this paper, a novel online low-rank representation subspace learning method is proposed for both large-scale and dynamic data. ...
Bo Li is partially funded by natural science foundation of China (NSFC) (61562062, 61762064, 61262050), Risheng Liu is partially funded by NSFC (61672125, 61300086, and 61632019) ...
doi:10.1109/tip.2017.2760510
pmid:28991739
fatcat:yaob7kbh65f57nat7f5gy6jzs4
Adaptive Structure-constrained Robust Latent Low-Rank Coding for Image Recovery
[article]
2019
arXiv
pre-print
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In this paper, we propose a robust representation learning model called Adaptive Structure-constrained Low-Rank Coding (AS-LRC) for the latent representation of data. ...
To recover the underlying subspaces more accurately, AS-LRC seamlessly integrates an adaptive weighting based block-diagonal structure-constrained low-rank representation and the group sparse salient feature ...
Since image data can usually be characterized by low-rank structures, robust lowrank subspace recovery and representation by minimizing the Nuclear-norm based formulation has arousing much attention in ...
arXiv:1908.07860v2
fatcat:xbv2ybchqfe33jukjq3c7usmtu
Low-Rank-Sparse Subspace Representation for Robust Regression
2017
2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)
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To address this issue, we propose a low-rank-sparse subspace representation for robust regression, hereafter referred to as LRS-RR in this paper. ...
The main contribution include the following: (1) Unlike most of the existing regression methods, we propose an approach with two phases of low-rank-sparse subspace recovery and regression optimization ...
Second, we propose a low-rank-sparse regression method via the framework of Low Rank subspace Sparse Representation (LRSR) by a supervised manner. ...
doi:10.1109/cvpr.2017.317
dblp:conf/cvpr/ZhangSGC17
fatcat:2l3utpvmpbcspcefxj5iwn63nm
Robust Subspace Recovery via Bi-Sparsity Pursuit
[article]
2014
arXiv
pre-print
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Nevertheless, the underlying structure may be affected by sparse errors and/or outliers. ...
Successful applications of sparse models in computer vision and machine learning imply that in many real-world applications, high dimensional data is distributed in a union of low dimensional subspaces ...
In [11] , a low-rank representation (LRR) recovers subspace structures from sample-specific corruptions by pursuing the lowest-rank representation of all data jointly. ...
arXiv:1403.8067v2
fatcat:zko7ckhw3rdbngpqo6pvzye73a
Introduction to the Issue on Robust Subspace Learning and Tracking: Theory, Algorithms, and Applications
2018
IEEE Journal on Selected Topics in Signal Processing
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By using a new tensor nuclear norm that extends the conventional TNN, Liu et al. better extract the low-rank tensor components in multi-way data by investigating the low-rank structure for core tensor ...
Gitlin et al. improve K-Subspaces clustering algorithm with a robust subspace recovery (RSR) method known as Coherence Pursuit (CoP) to handle low-rank outliers with low computational complexity. ...
doi:10.1109/jstsp.2018.2879245
fatcat:z3ohqdl37nat3pjo65fzsf2ady
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. ...
For enhanced low-rank recovery and error correction, our method constructs a low-rank tensor subspace to reconstruct given images along row and column directions simultaneously by computing two low-rank ...
Acknowledgements This work is partially supported by the National Natural Science ...
doi:10.1016/j.knosys.2015.06.001
fatcat:ggik3r5jafcqpjezziu3igd2ke
Relations among Some Low Rank Subspace Recovery Models
[article]
2014
arXiv
pre-print
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In recent years, there has been a lot of work that models subspace recovery as low rank minimization problems. ...
We find that some representative models, such as Robust Principal Component Analysis (R-PCA), Robust Low Rank Representation (R-LRR), and Robust Latent Low Rank Representation (R-LatLRR), are actually ...
Robust Low Rank Representation (Robust Shape Interaction and Low Rank Subspace Clustering) As mentioned above, LRR uses the data matrix itself as the dictionary to represent data samples. ...
arXiv:1412.2196v1
fatcat:iar574ptmzhmfcnqfh4vs5lzjm
Collaborative representation-based robust face recognition by discriminative low-rank representation
[article]
2019
arXiv
pre-print
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To alleviate the aforementioned problems to some extent, in this paper, we propose a discriminative low-rank representation method for collaborative representation-based (DLRR-CR) robust face recognition ...
Performance of conventional subspace learning methods and recently proposed sparse representation based classification (SRC) might be degraded when corrupted training samples are provided. ...
Acknowledgments This work was supported by the National Natural Science Foundation of
References ...
arXiv:1912.07778v1
fatcat:xt5ibbubszgjdkwfxooo72nf7y
Multilayer Collaborative Low-Rank Coding Network for Robust Deep Subspace Discovery
[article]
2020
arXiv
pre-print
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2019 pre-print arXiv:1912.06450v2 fatcat:r5dsikb2abcdzc7qzbpo7rqciiOther Versions
For subspace recovery, most existing low-rank representation (LRR) models performs in the original space in single-layer mode. ...
As such, the coher-ence issue can be also resolved due to the low-rank dictionary, and the robustness against noise can also be enhanced in the feature subspace. ...
ACKNOWLEDGEMENTS This work is partially supported by the National Natural Science Foundation of China (61672365, 61732008, 61725203, 61622305, 61871444 and 61806035) and the Fundamental Research Funds ...
arXiv:1912.06450v3
fatcat:63weg3s45ngxvizgt6pgj2bh5e
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