The Kendall and Mallows Kernels for Permutations

Yunlong Jiao (1, 2) , Jean-Philippe Vert (1, 2)

1 CBIO - Centre de Bioinformatique
2 Cancer et génome: Bioinformatique, biostatistiques et épidémiologie d'un système complexe

We show that the widely used Kendall tau correlation coefficient, and the related Mallows kernel, are positive definite kernels for permutations. They offer computationally attractive alternatives to more complex kernels on the symmetric group to learn from rankings, or learn to rank. We show how to extend these kernels to partial rankings, multivariate rankings and uncertain rankings. Examples are presented on how to formulate typical problems of learning from rankings such that they can be solved with state-of-the-art kernel algorithms. We demonstrate promising results on clustering heterogeneous rank data and high-dimensional classification problems in biomedical applications.

Mots clés: Kernel methods; Ranking learning; Computational biology; Machine learning

Domaines: Machine Learning [stat.ML]

Yunlong Jiao, Jean-Philippe Vert. The Kendall and Mallows Kernels for Permutations. 2016. ⟨hal-01279273v2⟩