Subspace Clustering with Priors via Sparse Quadratically Constrained Quadratic Programming

This paper considers the problem of recovering a subspace arrangement from noisy samples, potentially corrupted with outliers. Our main result shows that this problem can be formulated as a convex semi-definite optimization problem subject to an additional rank constrain that involves only a very sm...

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Published in:2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) pp. 5204 - 5212
Main Authors: Yongfang Cheng, Yin Wang, Sznaier, Mario, Camps, Octavia
Format: Conference Proceeding
Language:English
Published: IEEE 01.06.2016
Subjects:
Clustering algorithms
Computational complexity
Image segmentation
Noise measurement
Robustness
Symmetric matrices
ISSN:1063-6919
Online Access:Get full text
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Abstract This paper considers the problem of recovering a subspace arrangement from noisy samples, potentially corrupted with outliers. Our main result shows that this problem can be formulated as a convex semi-definite optimization problem subject to an additional rank constrain that involves only a very small number of variables. This is established by first reducing the problem to a quadratically constrained quadratic problem and then using its special structure to find conditions guaranteeing that a suitably built convex relaxation is indeed exact. When combined with the standard nuclear norm relaxation for rank, the results above lead to computationally efficient algorithms with optimality guarantees. A salient feature of the proposed approach is its ability to incorporate existing a-priori information about the noise, co-ocurrences, and percentage of outliers. These results are illustrated with several examples.
AbstractList This paper considers the problem of recovering a subspace arrangement from noisy samples, potentially corrupted with outliers. Our main result shows that this problem can be formulated as a convex semi-definite optimization problem subject to an additional rank constrain that involves only a very small number of variables. This is established by first reducing the problem to a quadratically constrained quadratic problem and then using its special structure to find conditions guaranteeing that a suitably built convex relaxation is indeed exact. When combined with the standard nuclear norm relaxation for rank, the results above lead to computationally efficient algorithms with optimality guarantees. A salient feature of the proposed approach is its ability to incorporate existing a-priori information about the noise, co-ocurrences, and percentage of outliers. These results are illustrated with several examples.
Author Yongfang Cheng
Yin Wang
Camps, Octavia
Sznaier, Mario
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  surname: Yin Wang
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  givenname: Mario
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  givenname: Octavia
  surname: Camps
  fullname: Camps, Octavia
  email: camps@coe.neu.edu
  organization: Electr. & Comput. Eng., Northeastern Univ., Boston, MA, USA
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Snippet This paper considers the problem of recovering a subspace arrangement from noisy samples, potentially corrupted with outliers. Our main result shows that this...
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StartPage 5204
SubjectTerms Clustering algorithms
Computational complexity
Image segmentation
Noise measurement
Robustness
Symmetric matrices
Title Subspace Clustering with Priors via Sparse Quadratically Constrained Quadratic Programming
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