Learning with Groups of Kernels

Marie Szafranski (1) , Yves Grandvalet (1) , Alain Rakotomamonjy (2)

1 Heudiasyc - Heuristique et Diagnostic des Systèmes Complexes [Compiègne]
2 LITIS - Laboratoire d'Informatique, de Traitement de l'Information et des Systèmes

The Support Vector Machine (SVM) is an acknowledged powerful tool for building classifiers, but it lacks flexibility, in the sense that the kernel is chosen prior to learning. Multiple Kernel Learning (MKL) enables to learn the kernel, from an ensemble of basis kernels, whose combination is optimized in the learning process. Here, we build on MKL to address the situations where there is a group structure among kernels that is believed to be relevant for the classification task. We develop the theoretical and the algorithmic aspects of learning with groups of kernels. Our formulation of the learning problem encompasses several setups, including MKL, where more or less emphasis is given to the group structure. We characterize the convexity of the learning problem, and provide a general wrapper algorithm for computing solutions. Finally, some experiments illustrate the behavior of several instances of our method.

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Marie Szafranski, Yves Grandvalet, Alain Rakotomamonjy. Learning with Groups of Kernels. Conférence d'Apprentissage (CAp), May 2008, Porquerolles, France. pp.à définir. ⟨hal-00275478⟩