Bi-sparsity pursuit: A paradigm for robust subspace recovery

Bian, Xiao; Panahi, Ashkan; Krim, Hamid

doi:10.1016/j.sigpro.2018.05.024

Title: Bi-sparsity pursuit: A paradigm for robust subspace recovery

Abstract

The success of sparse models in computer vision and machine learning is due to the fact that, high dimensional data is distributed in a union of low dimensional subspaces in many real-world applications. The underlying structure may, however, be adversely affected by sparse errors. 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 the presence of sparse corruptions. We further show the effectiveness of our method by experiments on real-world vision data.

Authors:

Bian, Xiao ^[1];

^[1]; Krim, Hamid ^[1]

North Carolina State University, Raleigh, NC (United States)

Publication Date:: Fri May 25 00:00:00 EDT 2018

Research Org.:: North Carolina State University, Raleigh, NC (United States)

Sponsoring Org.:: USDOE National Nuclear Security Administration (NNSA)

OSTI Identifier:: 1614542

Alternate Identifier(s):: OSTI ID: 1548246

Grant/Contract Number:: NA0002576

Resource Type:: Accepted Manuscript

Journal Name:: Signal Processing

Additional Journal Information:: Journal Volume: 152; Journal ID: ISSN 0165-1684

Publisher:: Elsevier

Country of Publication:: United States

Language:: English

Subject:: 42 ENGINEERING; signal recovery; sparse learning; subspace modeling

Citation Formats


                    Bian, Xiao, Panahi, Ashkan, and Krim, Hamid. Bi-sparsity pursuit: A paradigm for robust subspace recovery.  United States: N. p., 2018. 
Web.  doi:10.1016/j.sigpro.2018.05.024.

Copy to clipboard


                    Bian, Xiao, Panahi, Ashkan, & Krim, Hamid. Bi-sparsity pursuit: A paradigm for robust subspace recovery.  United States.  https://doi.org/10.1016/j.sigpro.2018.05.024

Copy to clipboard


                    Bian, Xiao, Panahi, Ashkan, and Krim, Hamid. Fri .  
"Bi-sparsity pursuit: A paradigm for robust subspace recovery".  United States.  https://doi.org/10.1016/j.sigpro.2018.05.024.  https://www.osti.gov/servlets/purl/1614542.

Copy to clipboard


                    
@article{osti_1614542,

  title        = {Bi-sparsity pursuit: A paradigm for robust subspace recovery},

  author       = {Bian, Xiao and Panahi, Ashkan and Krim, Hamid},

  abstractNote = {The success of sparse models in computer vision and machine learning is due to the fact that, high dimensional data is distributed in a union of low dimensional subspaces in many real-world applications. The underlying structure may, however, be adversely affected by sparse errors. 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 the presence of sparse corruptions. We further show the effectiveness of our method by experiments on real-world vision data.},

  doi          = {10.1016/j.sigpro.2018.05.024},

  journal      = {Signal Processing},

  number       = ,

  volume       = 152,

  place        = {United States},

  year         = {Fri May 25 00:00:00 EDT 2018},

  month        = {Fri May 25 00:00:00 EDT 2018}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Accepted Manuscript (Publisher)

Accepted Manuscript (DOE)

Publisher's Version of Record

https://doi.org/10.1016/j.sigpro.2018.05.024

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 3 works

Citation information provided by
Web of Science

Save / Share:

Export Metadata

Save to My Library

Works referenced in this record:

Robust principal component analysis?
journal, May 2011

Candès, Emmanuel J.; Li, Xiaodong; Ma, Yi
Journal of the ACM, Vol. 58, Issue 3
DOI: 10.1145/1970392.1970395

Innovation Pursuit: A New Approach to Subspace Clustering
journal, December 2017

Rahmani, Mostafa; Atia, George K.
IEEE Transactions on Signal Processing, Vol. 65, Issue 23
DOI: 10.1109/TSP.2017.2749206

Robust subspace clustering
journal, April 2014

Soltanolkotabi, Mahdi; Elhamifar, Ehsan; Candès, Emmanuel J.
The Annals of Statistics, Vol. 42, Issue 2
DOI: 10.1214/13-AOS1199

Binary- and Multi-class Group Sparse Canonical Correlation Analysis for Feature Extraction and Classification
journal, October 2013

Zhang, Zhao; Zhao, Mingbo; Chow, Tommy W. S.
IEEE Transactions on Knowledge and Data Engineering, Vol. 25, Issue 10
DOI: 10.1109/TKDE.2012.217

Augmented Lagrange Multiplier Functions and Duality in Nonconvex Programming
journal, May 1974

Rockafellar, R. Tyrrell
SIAM Journal on Control, Vol. 12, Issue 2
DOI: 10.1137/0312021

Unsupervised Activity Perception in Crowded and Complicated Scenes Using Hierarchical Bayesian Models
journal, March 2009

Xiaogang Wang, ; Grimson, W. E. L.
IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 31, Issue 3
DOI: 10.1109/TPAMI.2008.87

Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information
journal, February 2006

Candes, E.J.; Romberg, J.; Tao, T.
IEEE Transactions on Information Theory, Vol. 52, Issue 2, p. 489-509
DOI: 10.1109/TIT.2005.862083

Subspace Clustering via Optimal Direction Search
journal, December 2017

Rahmani, Mostafa; Atia, George K.
IEEE Signal Processing Letters, Vol. 24, Issue 12
DOI: 10.1109/LSP.2017.2757901

Sparse and Redundant Representation Modeling—What Next?
journal, December 2012

Elad, Michael
IEEE Signal Processing Letters, Vol. 19, Issue 12
DOI: 10.1109/LSP.2012.2224655

Playing with Duality: An overview of recent primal?dual approaches for solving large-scale optimization problems
journal, November 2015

Komodakis, Nikos; Pesquet, Jean-Christophe
IEEE Signal Processing Magazine, Vol. 32, Issue 6
DOI: 10.1109/MSP.2014.2377273

A geometric analysis of subspace clustering with outliers
journal, August 2012

Soltanolkotabi, Mahdi; Candés, Emmanuel J.
The Annals of Statistics, Vol. 40, Issue 4
DOI: 10.1214/12-AOS1034

On the Role of Sparse and Redundant Representations in Image Processing
journal, June 2010

Elad, Michael; Figueiredo, Mário A. T.; Ma, Yi
Proceedings of the IEEE, Vol. 98, Issue 6
DOI: 10.1109/JPROC.2009.2037655

Robust Recovery of Subspace Structures by Low-Rank Representation
journal, January 2013

Liu, Guangcan; Lin, Zhouchen; Yan, Shuicheng
IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 35, Issue 1
DOI: 10.1109/TPAMI.2012.88

Sparse Subspace Clustering: Algorithm, Theory, and Applications
journal, November 2013

Elhamifar, E.; Vidal, R.
IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 35, Issue 11
DOI: 10.1109/TPAMI.2013.57

Sparse Representation for Computer Vision and Pattern Recognition
journal, June 2010

Wright, John; Ma, Yi; Mairal, Julien
Proceedings of the IEEE, Vol. 98, Issue 6
DOI: 10.1109/JPROC.2010.2044470

A First-Order Primal-Dual Algorithm for Convex Problems with Applications to Imaging
journal, December 2010

Chambolle, Antonin; Pock, Thomas
Journal of Mathematical Imaging and Vision, Vol. 40, Issue 1
DOI: 10.1007/s10851-010-0251-1

Works referencing / citing this record:

Robust Group Subspace Recovery: A New Approach for Multi-Modality Data Fusion
journal, October 2020

Ghanem, Sally; Panahi, Ashkan; Krim, Hamid
IEEE Sensors Journal, Vol. 20, Issue 20
DOI: 10.1109/jsen.2020.2999461

Similar Records in DOE PAGES and OSTI.GOV collections:

BI-sparsity pursuit for robust subspace recovery

Journal Article Bian, Xiao ; Krim, Hamid - Conference: IEEE conference on Image Processing (ICIP)

Here, the success of sparse models in computer vision and machine learning in many real-world applications, may be attributed in large part, to the fact that many high dimensional data are distributed in a union of low dimensional subspaces. The underlying structure may, however, be adversely affected by sparse errors, thus inducing additional complexity in recovering it. In this paper, we propose a bi-sparse model as a framework to investigate and analyze this problem, and provide as a result , a novel algorithm to recover the union of subspaces in presence of sparse corruptions. We additionally demonstrate the effectiveness ofmore »« less
https://doi.org/10.1109/ICIP.2015.7351462

Full Text Available
Robust Group Subspace Recovery: A New Approach for Multi-Modality Data Fusion

Journal Article Ghanem, Sally ; Panahi, Ashkan ; Krim, Hamid ; ... - IEEE Sensors Journal

Robust Subspace Recovery (RoSuRe) algorithm was recently introduced as a principled and numerically efficient algorithm that unfolds underlying Unions of Subspaces (UoS) structure, present in the data. The union of Subspaces (UoS) is capable of identifying more complex trends in data sets than simple linear models. In this work, we build on and extend RoSuRe to prospect the structure of different data modalities individually. We propose a novel multi-modal data fusion approach based on group sparsity which we refer to as Robust Group Subspace Recovery (RoGSuRe). Relying on a bi-sparsity pursuit paradigm and non-smooth optimization techniques, the introduced framework learnsmore »« less
https://doi.org/10.1109/jsen.2020.2999461

Full Text Available
Sparsity and Nullity: Paradigms for Analysis Dictionary Learning

Journal Article Bian, Xiao ; Krim, Hamid ; Bronstein, Alex ; ... - SIAM Journal on Imaging Sciences

Sparse models in dictionary learning have been successfully applied in a wide variety of machine learning and computer vision problems, and as a result have recently attracted increased research interest. Another interesting related problem based on linear equality constraints, namely the sparse null space (SNS) problem, first appeared in 1986 and has since inspired results on sparse basis pursuit. In this work, we investigate the relation between the SNS problem and the analysis dictionary learning (ADL) problem, and show that the SNS problem plays a central role, and may be utilized to solve dictionary learning problems. Moreover, we propose anmore »« less
https://doi.org/10.1137/15M1030376
Beyond union of subspaces: Subspace pursuit on Grassmann manifold for data representation

Journal Article Shen, Xinyue ; Krim, Hamid ; Gu, Yuantao - 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

Discovering the underlying structure of a high-dimensional signal or big data has always been a challenging topic, and has become harder to tackle especially when the observations are exposed to arbitrary sparse perturbations. Here in this paper, built on the model of a union of subspaces (UoS) with sparse outliers and inspired by a basis pursuit strategy, we exploit the fundamental structure of a Grassmann manifold, and propose a new technique of pursuing the subspaces systematically by solving a non-convex optimization problem using the alternating direction method of multipliers. This problem as noted is further complicated by non-convex constraints onmore »« less
https://doi.org/10.1109/ICASSP.2016.7472444

Full Text Available
Anomaly Detection in Moving-Camera Video Sequences Using Principal Subspace Analysis

Journal Article Thomaz, Lucas A. ; Jardim, Eric ; da Silva, Allan F. ; ... - IEEE Transactions on Circuits and Systems I: Regular Papers

This study presents a family of algorithms based on sparse decompositions that detect anomalies in video sequences obtained from slow moving cameras. These algorithms start by computing the union of subspaces that best represents all the frames from a reference (anomaly free) video as a low-rank projection plus a sparse residue. Then, they perform a low-rank representation of a target (possibly anomalous) video by taking advantage of both the union of subspaces and the sparse residue computed from the reference video. Such algorithms provide good detection results while at the same time obviating the need for previous video synchronization. However,more »« less
Cited by 13
https://doi.org/10.1109/TCSI.2017.2758379

Full Text Available

Similar Records

Title: Bi-sparsity pursuit: A paradigm for robust subspace recovery

Abstract

Citation Formats

Robust principal component analysis? journal, May 2011

Innovation Pursuit: A New Approach to Subspace Clustering journal, December 2017

Robust subspace clustering journal, April 2014

Binary- and Multi-class Group Sparse Canonical Correlation Analysis for Feature Extraction and Classification journal, October 2013

Augmented Lagrange Multiplier Functions and Duality in Nonconvex Programming journal, May 1974

Unsupervised Activity Perception in Crowded and Complicated Scenes Using Hierarchical Bayesian Models journal, March 2009

Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information journal, February 2006

Subspace Clustering via Optimal Direction Search journal, December 2017

Sparse and Redundant Representation Modeling—What Next? journal, December 2012

Playing with Duality: An overview of recent primal?dual approaches for solving large-scale optimization problems journal, November 2015

A geometric analysis of subspace clustering with outliers journal, August 2012

On the Role of Sparse and Redundant Representations in Image Processing journal, June 2010

Robust Recovery of Subspace Structures by Low-Rank Representation journal, January 2013

Sparse Subspace Clustering: Algorithm, Theory, and Applications journal, November 2013

Sparse Representation for Computer Vision and Pattern Recognition journal, June 2010

A First-Order Primal-Dual Algorithm for Convex Problems with Applications to Imaging journal, December 2010

Robust Group Subspace Recovery: A New Approach for Multi-Modality Data Fusion journal, October 2020

Robust principal component analysis?
journal, May 2011

Innovation Pursuit: A New Approach to Subspace Clustering
journal, December 2017

Robust subspace clustering
journal, April 2014

Binary- and Multi-class Group Sparse Canonical Correlation Analysis for Feature Extraction and Classification
journal, October 2013

Augmented Lagrange Multiplier Functions and Duality in Nonconvex Programming
journal, May 1974

Unsupervised Activity Perception in Crowded and Complicated Scenes Using Hierarchical Bayesian Models
journal, March 2009

Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information
journal, February 2006

Subspace Clustering via Optimal Direction Search
journal, December 2017

Sparse and Redundant Representation Modeling—What Next?
journal, December 2012

Playing with Duality: An overview of recent primal?dual approaches for solving large-scale optimization problems
journal, November 2015

A geometric analysis of subspace clustering with outliers
journal, August 2012

On the Role of Sparse and Redundant Representations in Image Processing
journal, June 2010

Robust Recovery of Subspace Structures by Low-Rank Representation
journal, January 2013

Sparse Subspace Clustering: Algorithm, Theory, and Applications
journal, November 2013

Sparse Representation for Computer Vision and Pattern Recognition
journal, June 2010

A First-Order Primal-Dual Algorithm for Convex Problems with Applications to Imaging
journal, December 2010

Robust Group Subspace Recovery: A New Approach for Multi-Modality Data Fusion
journal, October 2020