Semidefinite and Spectral Relaxations for Multi-Label Classification

Rémi Lajugie 1, 2 Piotr Bojanowski 3, 2 Sylvain Arlot 1, 2 Francis Bach 1, 2
1 SIERRA - Statistical Machine Learning and Parsimony
DI-ENS - Département d'informatique de l'École normale supérieure, ENS Paris - École normale supérieure - Paris, Inria Paris-Rocquencourt, CNRS - Centre National de la Recherche Scientifique : UMR8548
3 WILLOW - Models of visual object recognition and scene understanding
DI-ENS - Département d'informatique de l'École normale supérieure, ENS Paris - École normale supérieure - Paris, Inria Paris-Rocquencourt, CNRS - Centre National de la Recherche Scientifique : UMR8548
Abstract : In this paper, we address the problem of multi-label classification. We consider linear classifiers and propose to learn a prior over the space of labels to directly leverage the performance of such methods. This prior takes the form of a quadratic function of the labels and permits to encode both attractive and repulsive relations between labels. We cast this problem as a structured prediction one aiming at optimizing either the accuracies of the predictors or the F 1-score. This leads to an optimization problem closely related to the max-cut problem, which naturally leads to semidefinite and spectral relaxations. We show on standard datasets how such a general prior can improve the performances of multi-label techniques.
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Preprints, Working Papers, ...
2015
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https://hal.inria.fr/hal-01159321
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Submitted on : Wednesday, June 3, 2015 - 4:22:05 PM
Last modification on : Thursday, September 29, 2016 - 1:22:40 AM
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  • HAL Id : hal-01159321, version 1
  • ARXIV : 1506.01829

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Rémi Lajugie, Piotr Bojanowski, Sylvain Arlot, Francis Bach. Semidefinite and Spectral Relaxations for Multi-Label Classification. 2015. <hal-01159321>

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