Learning Theory and Kernel Machines

Volume 2777 of the series Lecture Notes in Computer Science pp 173-187

Comparing Clusterings by the Variation of Information

  • Marina MeilăAffiliated withUniversity of Washington

* Final gross prices may vary according to local VAT.

Get Access


This paper proposes an information theoretic criterion for comparing two partitions, or clusterings, of the same data set. The criterion, called variation of information (VI), measures the amount of information lost and gained in changing from clustering \({\cal C}\) to clustering \({\cal C}'\). The criterion makes no assumptions about how the clusterings were generated and applies to both soft and hard clusterings. The basic properties of VI are presented and discussed from the point of view of comparing clusterings. In particular, the VI is positive, symmetric and obeys the triangle inequality. Thus, surprisingly enough, it is a true metric on the space of clusterings.


Clustering Comparing partitions Measures of agreement Information theory Mutual information