Statistic complexity: combining kolmogorov complexity with an ensemble approach.
BACKGROUND
The evaluation of the complexity of an observed object is an old but outstanding problem. In this paper we are tying on this problem introducing a measure called statistic complexity.


RESULTS
This complexity measure is different to all other measures in the following senses. First, it is a bivariate measure that compares two objects, corresponding to pattern generating processes, on the basis of the normalized compression distance with each other. Second, it provides the quantification of an error that could have been encountered by comparing samples of finite size from the underlying processes. Hence, the statistic complexity provides a statistical quantification of the statement ' is similarly complex as Y'.


CONCLUSIONS
The presented approach, ultimately, transforms the classic problem of assessing the complexity of an object into the realm of statistics. This may open a wider applicability of this complexity measure to diverse application areas.
Emmert-Streib
Frank
F
Computational Biology and Machine Learning, Center for Cancer Research and Cell Biology, School of Medicine, Dentistry and Biomedical Sciences, Queen's University Belfast, Belfast, United Kingdom. v@bio-complexity.com
D000465:Algorithms; D000704:Analysis of Variance; D013223:Statistics as Topic / Q000379:methods* / Q000592:standards