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
2 DI-ENS - Département d'informatique - ENS Paris
3 WILLOW - Models of visual object recognition and scene understanding

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.

Domains: Machine Learning [cs.LG]

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