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Sparse subspace clustering

Ehsan Elhamifar, Rene Vidal
2009 2009 IEEE Conference on Computer Vision and Pattern Recognition  
We propose a method based on sparse representation (SR) to cluster data drawn from multiple low-dimensional linear or affine subspaces embedded in a high-dimensional space.  ...  The segmentation of the data is obtained by applying spectral clustering to a similarity matrix built from this SR. Our method can handle noise, outliers as well as missing data.  ...  We have presented a novel approach to subspace clustering based on sparse representation.  ... 
doi:10.1109/cvpr.2009.5206547 dblp:conf/cvpr/ElhamifarV09 fatcat:wlbox6rlpfhrzobtdm6fekelwa

Sparse subspace clustering

E. Elhamifar, R. Vidal
2009 2009 IEEE Conference on Computer Vision and Pattern Recognition  
We propose a method based on sparse representation (SR) to cluster data drawn from multiple low-dimensional linear or affine subspaces embedded in a high-dimensional space.  ...  The segmentation of the data is obtained by applying spectral clustering to a similarity matrix built from this SR. Our method can handle noise, outliers as well as missing data.  ...  We have presented a novel approach to subspace clustering based on sparse representation.  ... 
doi:10.1109/cvprw.2009.5206547 fatcat:3yogs2jzirhl3npbdj4i2f7rmq

Greedy algorithm for subspace clustering from corrupted and incomplete data

Alexander Petukhov, Inna Kozlov
2015 2015 International Conference on Sampling Theory and Applications (SampTA)  
The main difference of our algorithm from predecessors is its ability to work with noisy data having a high rate of erasures (missed entries at the known locations) and errors (corrupted entries at unknown  ...  We describe the Fast Greedy Sparse Subspace Clustering (FGSSC) algorithm providing an efficient method for clustering data belonging to a few low-dimensional linear or affine subspaces.  ...  FGSSC has significantly increased resilience to the corruption of entries on sparse set, to the data incompleteness, and to noise.  ... 
doi:10.1109/sampta.2015.7148933 fatcat:5yiwgv47vfcu5eo5fgnefyr45u

Sparse Subspace Clustering: Algorithm, Theory, and Applications

E. Elhamifar, R. Vidal
2013 IEEE Transactions on Pattern Analysis and Machine Intelligence  
In this paper, we propose and study an algorithm, called sparse subspace clustering, to cluster data points that lie in a union of low-dimensional subspaces.  ...  Another key advantage of the proposed algorithm with respect to the state of the art is that it can deal directly with data nuisances, such as noise, sparse outlying entries, and missing entries, by incorporating  ...  ACKNOWLEDGMENTS This work was partially supported by US National Science Foundation grants NSF-ISS 0447739 and NSF-CSN 0931805.  ... 
doi:10.1109/tpami.2013.57 pmid:24051734 fatcat:34st7xdfw5gadp2ud5r3f7kzhm

Fast greedy algorithm for subspace clustering from corrupted and incomplete data [article]

Alexander Petukhov, Inna Kozlov
2013 arXiv   pre-print
The main difference of our algorithm from predecessors is its ability to work with noisy data having a high rate of erasures (missed entries with the known coordinates) and errors (corrupted entries with  ...  We describe the Fast Greedy Sparse Subspace Clustering (FGSSC) algorithm providing an efficient method for clustering data belonging to a few low-dimensional linear or affine subspaces.  ...  We assume that those data may be corrupted with sparse errors, random noise is distributed over all vector entries, and a quite significant part of data is missing.  ... 
arXiv:1306.1716v1 fatcat:zk3zsugdvjh4fcr4reuzltvyou

Subspace Segmentation by Successive Approximations: A Method for Low-Rank and High-Rank Data with Missing Entries [article]

João Carvalho, Manuel Marques, João P. Costeira
2017 arXiv   pre-print
Exploring the sparse representation model, we jointly estimate the missing data while imposing the intrinsic subspace structure.  ...  We propose a method to reconstruct and cluster incomplete high-dimensional data lying in a union of low-dimensional subspaces.  ...  We build upon the work Sparse Subspace Clustering [10] and explicitly represent the missing data.  ... 
arXiv:1709.01467v1 fatcat:g5pzersjcncq7mron4bga3uvby

Sparse Subspace Clustering: Algorithm, Theory, and Applications [article]

Ehsan Elhamifar, Rene Vidal
2013 arXiv   pre-print
In this paper, we propose and study an algorithm, called Sparse Subspace Clustering (SSC), to cluster data points that lie in a union of low-dimensional subspaces.  ...  Another key advantage of the proposed algorithm with respect to the state of the art is that it can deal with data nuisances, such as noise, sparse outlying entries, and missing entries, directly by incorporating  ...  ACKNOWLEDGMENT The authors would like to thank the financial support of grants nsf-iss 0447739 and nsf-csn 0931805.  ... 
arXiv:1203.1005v3 fatcat:re7bnzvcaneyviwdq3u3ehsqyi

Greedy Approach for Subspace Clustering from Corrupted and Incomplete Data [article]

Alexander Petukhov, Inna Kozlov
2013 arXiv   pre-print
We describe the Greedy Sparse Subspace Clustering (GSSC) algorithm providing an efficient method for clustering data belonging to a few low-dimensional linear or affine subspaces from incomplete corrupted  ...  and noisy data.  ...  Vice versa, we assume that those data are corrupted with sparse errors, random noise distributed over all vector entries and quite significant part of data is missed.  ... 
arXiv:1304.4282v1 fatcat:6am6egmo45dxlnp3foxtlls3qe

A Rank-Constrained Matrix Representation for Hypergraph-Based Subspace Clustering

Yubao Sun, Zhi Li, Min Wu
2015 Mathematical Problems in Engineering  
Real-world data are frequently corrupted with both sparse error and noise.  ...  This paper presents a novel, rank-constrained matrix representation combined with hypergraph spectral analysis to enable the recovery of the original subspace structures of corrupted data.  ...  Sparse-based methods utilize low-rank and sparse properties of the data for subspace clustering.  ... 
doi:10.1155/2015/572753 fatcat:7hjwtyx2l5hb5nf4plmzc4fcnq

Robust Subspace Recovery via Bi-Sparsity Pursuit [article]

Xiao Bian, Hamid Krim
2014 arXiv   pre-print
In this paper, we propose a bi-sparse model as a framework to analyze this problem and provide a novel algorithm to recover the union of subspaces in presence of sparse corruptions.  ...  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  ...  This result validates the effectiveness of our method to solve the problem of subspace clustering with sparsely corrupted data.  ... 
arXiv:1403.8067v2 fatcat:zko7ckhw3rdbngpqo6pvzye73a

Robust Trajectory Clustering for Motion Segmentation

Feng Shi, Zhong Zhou, Jiangjian Xiao, Wei Wu
2013 2013 IEEE International Conference on Computer Vision  
results against severe data missing and noises.  ...  To cluster such corrupted point based trajectories into multiple motions is still a hard problem.  ...  a large number of missing and corrupted data.  ... 
doi:10.1109/iccv.2013.383 dblp:conf/iccv/ShiZXW13 fatcat:f3nru43rqzfwpfjgriiku25lxm

Low-Rank Representation for Incomplete Data

Jiarong Shi, Wei Yang, Longquan Yong, Xiuyun Zheng
2014 Mathematical Problems in Engineering  
Low-rank matrix recovery (LRMR) has been becoming an increasingly popular technique for analyzing data with missing entries, gross corruptions, and outliers.  ...  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.  ...  For the datasets with missing entries and large sparse corruption, the robust recovery of subspace structures may be a challenging task.  ... 
doi:10.1155/2014/439417 fatcat:3jp53soycbhhlnudcfd4yhnmuy

Sparse Subspace Clustering with Missing Entries

Congyuan Yang, Daniel P. Robinson, René Vidal
2015 International Conference on Machine Learning  
Experiments on synthetic and real data show the advantages and disadvantages of the proposed methods, which all outperform the natural approach (low-rank matrix completion followed by sparse subspace clustering  ...  The first one generalizes the sparse subspace clustering algorithm so that it can obtain a sparse representation of the data using only the observed entries.  ...  René Vidal also thanks Li Chunguang, Chong You, Mahdi Soltanolkotabi, Lester Mackey, and Emmanuel Candès for extremely insightful discussions on the problem of subspace clustering with missing data.  ... 
dblp:conf/icml/YangRV15 fatcat:wxjxv2al3ncv7cxoutvb67dp3m

Motion segmentation via robust subspace separation in the presence of outlying, incomplete, or corrupted trajectories

Shankar R. Rao, Roberto Tron, Rene Vidal, Yi Ma
2008 2008 IEEE Conference on Computer Vision and Pattern Recognition  
Our methods draw strong connections between lossy compression, rank minimization, and sparse representation.  ...  In this paper, we develop a robust subspace separation scheme that can deal with all of these practical issues in a unified framework.  ...  We assume that we have a set of samples Y ∈ R D×P on the N subspaces with no missing entries, and we use Y to complete each sample with missing entries individually.  ... 
doi:10.1109/cvpr.2008.4587437 dblp:conf/cvpr/RaoTVM08 fatcat:2txvoe6voje4dm3bii3oyurwc4

Subspace Clustering with Missing and Corrupted Data [article]

Zachary Charles, Amin Jalali, Rebecca Willett
2018 arXiv   pre-print
In this paper, we study a robust variant of SSC and establish clustering guarantees in the presence of corrupted or missing data.  ...  One popular approach, sparse subspace clustering (SSC), represents each sample as a weighted combination of the other samples, with weights of minimal ℓ_1 norm, and then uses those learned weights to cluster  ...  for subspace clustering with missing data.  ... 
arXiv:1707.02461v2 fatcat:42cosabkhzg35p4zpe4pzi3rb4
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