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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Bibliographic Details
Published in2016 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
LanguageEnglish
Published IEEE 01.06.2016
Subjects
Clustering algorithms
Computational complexity
Image segmentation
Noise measurement
Robustness
Symmetric matrices
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Summary: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.
ISSN:1063-6919
DOI:10.1109/CVPR.2016.562