Publications [#264700] of Guillermo Sapiro

Papers Published

1. Qiu, Q; Sapiro, G, Learning Transformations, 2014 IEEE International Conference on Image Processing, ICIP 2014 (January, 2014), pp. 4008-4012, IEEE, ISBN 9781479957514 [doi]
   (last updated on 2024/04/25)

   Abstract:
   A low-rank transformation learning framework for subspace clustering and classification is here proposed. Many high-dimensional data, such as face images and motion sequences, approximately lie in a union of low-dimensional subspaces. The corresponding subspace clustering problem has been extensively studied in the literature, partitioning such high-dimensional data into clusters corresponding to their underlying low-dimensional subspaces. However, low-dimensional intrinsic structures are often violated for real-world 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 low-rank structure for data from the same subspace, and, at the same time, forces a high-rank 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.