Shape interaction matrix revisited and robustified: efficient subspace clustering with corrupted and incomplete data
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Date
2015
Authors
Ji, P.
Salzmann, M.
Li, H.
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Conference paper
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Proceedings / IEEE International Conference on Computer Vision. IEEE International Conference on Computer Vision, 2015, pp.4687-4695
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Pan Ji, Mathieu Salzmann, and Hongdong Li
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2015 IEEE International Conference on Computer Vision (ICCV 2015) (7 Dec 2015 - 13 Dec 2015 : Santiago, Chile)
Abstract
The Shape Interaction Matrix (SIM) is one of the earliest approaches to performing subspace clustering (i.e., separating points drawn from a union of subspaces). In this paper, we revisit the SIM and reveal its connections to several recent subspace clustering methods. Our analysis lets us derive a simple, yet effective algorithm to robustify the SIM and make it applicable to realistic scenarios where the data is corrupted by noise. We justify our method by intuitive examples and the matrix perturbation theory. We then show how this approach can be extended to handle missing data, thus yielding an efficient and general subspace clustering algorithm. We demonstrate the benefits of our approach over state-of-the-art subspace clustering methods on several challenging motion segmentation and face clustering problems, where the data includes corrupted and missing measurements.
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© 2015 IEEE