Title
Normalized Information Distance is Not Semicomputable
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.
Year
Venue
Keywords
2010
Computing Research Repository
semicomputability.,kolmogorov complexity,index terms— normalized information distance
Field
DocType
Volume
Discrete mathematics,Normalization (statistics),Kolmogorov complexity,Similarity measure,Information distance,Normalized compression distance,Algorithm,Cluster analysis,Mathematics
Journal
abs/1006.3
Citations 
PageRank 
References 
0
0.34
8
Authors
3
Name
Order
Citations
PageRank
Sebastiaan A. Terwijn118621.06
Leen Torenvliet229041.73
Paul Vitányi32130287.76