Lossy compression of permutations
Author(s)Wang, Da; Mazumdar, Arya; Wornell, Gregory W.
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We investigate the lossy compression of permutations by analyzing the trade-off between the size of a source code and the distortion with respect to Kendall tau distance, Spearman's footrule, Chebyshev distance and ℓ[subscript 1] distance of inversion vectors. We show that given two permutations, Kendall tau distance upper bounds the ℓ[subscript 1] distance of inversion vectors and a scaled version of Kendall tau distance lower bounds the ℓ[subscript 1] distance of inversion vectors with high probability, which indicates an equivalence of the source code designs under these two distortion measures. Similar equivalence is established for all the above distortion measures, every one of which has different operational significance and applications in ranking and sorting. These findings show that an optimal coding scheme for one distortion measure is effectively optimal for other distortion measures above.
DepartmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Proceedings of the 2014 IEEE International Symposium on Information Theory
Institute of Electrical and Electronics Engineers (IEEE)
Wang, Da, Arya Mazumdar, and Gregory W. Wornell. “Lossy Compression of Permutations.” 2014 IEEE International Symposium on Information Theory (June 2014).
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