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 learn to rank. We show how to...
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| Veröffentlicht in: | IEEE transactions on pattern analysis and machine intelligence 2018-07, Vol.40 (7), p.1755-1769 |
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| container_title | IEEE transactions on pattern analysis and machine intelligence |
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| creator | Yunlong Jiao Vert, Jean-Philippe |
| description | 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. |
| doi_str_mv | 10.1109/TPAMI.2017.2719680 |
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| ispartof | IEEE transactions on pattern analysis and machine intelligence, 2018-07, Vol.40 (7), p.1755-1769 |
| issn | 0162-8828 1939-3539 2160-9292 |
| language | eng |
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| source | IEEE Electronic Library (IEL) |
| subjects | Analytical models Bioinformatics Biomedical materials cluster analysis of rank data Clustering Correlation Correlation coefficients Data models Gene expression Kendall tau correlation Kernel Kernel functions Kernel methods Machine Learning Mallows model permutation Permutations Sorting State of the art Statistics supervised classification of biomedical data |
| title | The Kendall and Mallows Kernels for Permutations |
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