The Kendall and Mallows Kernels for Permutations

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 to learn to rank. We show how to extend the Kendall kernel to partial rankings or rankings with uncertainty, and demonstrate promising results on high-dimensional classification problems in biomedical applications.