Math @ Duke

Publications [#264700] of Guillermo Sapiro
Papers Published
 Qiu, Q; Sapiro, G; Qiu, Q; Sapiro, G, Learning TransformationsLearning Transformations,
2014 IEEE International Conference on Image Processing, ICIP 2014
(January, 2014),
pp. 40084012, ISBN 9781479957514 [doi]
(last updated on 2017/12/14)
Abstract: © 2014 IEEE. A lowrank transformation learning framework for subspace clustering and classification is here proposed. Many highdimensional data, such as face images and motion sequences, approximately lie in a union of lowdimensional subspaces. The corresponding subspace clustering problem has been extensively studied in the literature, partitioning such highdimensional data into clusters corresponding to their underlying lowdimensional subspaces. However, lowdimensional intrinsic structures are often violated for realworld observations, as they can be corrupted by errors or deviate from ideal models. We propose to address this by learning a linear transformation on subspaces using matrix rank, via its convex surrogate nuclear norm, as the optimization criteria. The learned linear transformation restores a lowrank structure for data from the same subspace, and, at the same time, forces a highrank structure for data from different subspaces. In this way, we reduce variations within the subspaces, and increase separation between the subspaces for improved subspace clustering and classification.


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