Lossy compression of permutations
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Wornell_Lossy compression.pdf
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237.59 KB
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Checksum (MD5)
2c7d37b1a85aec310ca7a77cbea39b75
Author(s)
Wang, Da
Mazumdar, Arya
Wornell, Gregory W.
Date Issued
June 2014
Journal
Proceedings of the 2014 IEEE International Symposium on Information Theory
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
Wang, Da, Arya Mazumdar, and Gregory W. Wornell. “Lossy Compression of Permutations.” 2014 IEEE International Symposium on Information Theory (June 2014).
Version
Author's final manuscript
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1109/ISIT.2014.6874785
