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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| Vydáno v: | 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) s. 5204 - 5212 |
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| Jazyk: | angličtina |
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01.06.2016
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| ISSN: | 1063-6919 |
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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. |
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| 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 |
| Author_xml | – sequence: 1 surname: Yongfang Cheng fullname: Yongfang Cheng email: cheng.yong@husky.neu.edu organization: Electr. & Comput. Eng., Northeastern Univ., Boston, MA, USA – sequence: 2 surname: Yin Wang fullname: Yin Wang email: wang.yin@husky.neu.edu organization: Electr. & Comput. Eng., Northeastern Univ., Boston, MA, USA – sequence: 3 givenname: Mario surname: Sznaier fullname: Sznaier, Mario email: msznaier@coe.neu.edu organization: Electr. & Comput. Eng., Northeastern Univ., Boston, MA, USA – sequence: 4 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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| 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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