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Type: Conference paper
Title: The k-support norm and convex envelopes of cardinality and rank
Author: Eriksson, A.
Pham, T.
Chin, T.
Reid, I.
Citation: Proceedings of the 2015 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2015 / vol.07-12-June-2015, pp.3349-3357
Publisher: IEEE
Issue Date: 2015
Series/Report no.: IEEE Conference on Computer Vision and Pattern Recognition
ISBN: 9781467369640
ISSN: 1063-6919
Conference Name: 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR 2015) (07 Jun 2015 - 12 Jun 2015 : Boston, MA)
Statement of
Anders Eriksson, Trung Thanh Pham, Tat-Jun Chin, Ian Reid
Abstract: Sparsity, or cardinality, as a tool for feature selection is extremely common in a vast number of current computer vision applications. The k-support norm is a recently proposed norm with the proven property of providing the tightest convex bound on cardinality over the Euclidean norm unit ball. In this paper we present a re-derivation of this norm, with the hope of shedding further light on this particular surrogate function. In addition, we also present a connection between the rank operator, the nuclear norm and the k-support norm. Finally, based on the results established in this re-derivation, we propose a novel algorithm with significantly improved computational efficiency, empirically validated on a number of different problems, using both synthetic and real world data.
Keywords: Optimization, computer science, computer vision, computational modeling, convex functions, convergence, electrical engineering
Rights: © 2015 IEEE
RMID: 0030046341
DOI: 10.1109/CVPR.2015.7298956
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Appears in Collections:Computer Science publications

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