The Kendall and Mallows Kernels for Permutations


Yunlong Jiao, Jean-Philippe Vert ;
Proceedings of the 32nd International Conference on Machine Learning, PMLR 37:1935-1944, 2015.


We show that the widely used Kendall tau correlation coefficient is a positive definite kernel for permutations. It offers a computationally attractive alternative to more complex kernels on the symmetric group to learn from rankings, or to learn to rank. We show how to extend it to partial rankings or rankings with uncertainty, and demonstrate promising results on high-dimensional classification problems in biomedical applications.

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