Normalized Information Distance is Not Semicomputable
Computational Complexity
2010-06-17 v1 Computer Vision and Pattern Recognition
Data Analysis, Statistics and Probability
Abstract
Normalized information distance (NID) uses the theoretical notion of Kolmogorov complexity, which for practical purposes is approximated by the length of the compressed version of the file involved, using a real-world compression program. This practical application is called 'normalized compression distance' and it is trivially computable. It is a parameter-free similarity measure based on compression, and is used in pattern recognition, data mining, phylogeny, clustering, and classification. The complexity properties of its theoretical precursor, the NID, have been open. We show that the NID is neither upper semicomputable nor lower semicomputable.
Cite
@article{arxiv.1006.3275,
title = {Normalized Information Distance is Not Semicomputable},
author = {Sebastiaan A. Terwijn and Leen Torenvliet and Paul M. B. Vitanyi},
journal= {arXiv preprint arXiv:1006.3275},
year = {2010}
}
Comments
9 pages, LaTeX, No figures, To appear in J. Comput. Syst. Sci