Robust Subspace Recovery via Dual Sparsity Pursuit

Successful applications of sparse models in computer vision and machine learning [3][2][5] imply that in many real-world applications, high dimensional data is distributed in a union of low dimensional subspaces. Nevertheless, the underlying structure may be affected by sparse errors and/or outliers. In this paper, we propose a dual 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. We further show the effectiveness of our method by experiments on both synthetic data and real-world vision data.

[1]  Yong Yu,et al.  Robust Recovery of Subspace Structures by Low-Rank Representation , 2010, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[2]  W. Eric L. Grimson,et al.  Unsupervised Activity Perception in Crowded and Complicated Scenes Using Hierarchical Bayesian Models , 2008, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[3]  Guillermo Sapiro,et al.  See all by looking at a few: Sparse modeling for finding representative objects , 2012, 2012 IEEE Conference on Computer Vision and Pattern Recognition.

[4]  R. Vidal,et al.  Sparse Subspace Clustering: Algorithm, Theory, and Applications. , 2013, IEEE transactions on pattern analysis and machine intelligence.

[5]  David G. Luenberger,et al.  Linear and Nonlinear Programming: Second Edition , 2003 .

[6]  Michael Elad,et al.  K-SVD dictionary-learning for the analysis sparse model , 2012, 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[7]  Zhixun Su,et al.  Linearized Alternating Direction Method with Adaptive Penalty for Low-Rank Representation , 2011, NIPS.

[8]  R. Rockafellar.  Augmented Lagrange Multiplier Functions and Duality in Nonconvex Programming , 1974 .

[9]  Honglak Lee,et al.  Sparse deep belief net model for visual area V2 , 2007, NIPS.

[10]  Michael Elad,et al.  On the Role of Sparse and Redundant Representations in Image Processing , 2010, Proceedings of the IEEE.

[11]  Michael I. Jordan,et al.  On Spectral Clustering: Analysis and an algorithm , 2001, NIPS.

[12]  Michael Elad,et al.  Sparse and Redundant Representation Modeling—What Next? , 2012, IEEE Signal Processing Letters.

[13]  David J. Kriegman,et al.  Acquiring linear subspaces for face recognition under variable lighting , 2005, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[14]  Guillermo Sapiro,et al.  Sparse Representation for Computer Vision and Pattern Recognition , 2010, Proceedings of the IEEE.

[15]  René Vidal,et al.  Sparse subspace clustering , 2009, CVPR.

[16]  Yi Ma,et al.  Robust principal component analysis? , 2009, JACM.

[17]  Yi Ma,et al.  The Augmented Lagrange Multiplier Method for Exact Recovery of Corrupted Low-Rank Matrices , 2010, Journal of structural biology.

[18]  Emmanuel J. Candès,et al.  A Geometric Analysis of Subspace Clustering with Outliers , 2011, ArXiv.

[19]  Marc Pollefeys,et al.  A General Framework for Motion Segmentation: Independent, Articulated, Rigid, Non-rigid, Degenerate and Non-degenerate , 2006, ECCV.