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Comparing clusterings--an information based distance

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  • Meila, Marina
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    Abstract

    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 to clustering . The basic properties of VI are presented and discussed. We focus on two kinds of properties: (1) those that help one build intuition about the new criterion (in particular, it is shown the VI is a true metric on the space of clusterings), and (2) those that pertain to the comparability of VI values over different experimental conditions. As the latter properties have rarely been discussed explicitly before, other existing comparison criteria are also examined in their light. Finally we present the VI from an axiomatic point of view, showing that it is the only "sensible" criterion for comparing partitions that is both aligned to the lattice and convexely additive. As a consequence, we prove an impossibility result for comparing partitions: there is no criterion for comparing partitions that simultaneously satisfies the above two desirable properties and is bounded.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 98 (2007)
    Issue (Month): 5 (May)
    Pages: 873-895

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    Handle: RePEc:eee:jmvana:v:98:y:2007:i:5:p:873-895

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    Related research

    Keywords: Agreement measures Clustering Comparing partitions Information theory Mutual information Similarity measures;

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    Cited by:
    1. Isabella Morlini & Sergio Zani, 2012. "Dissimilarity and similarity measures for comparing dendrograms and their applications," Advances in Data Analysis and Classification, Springer, vol. 6(2), pages 85-105, July.
    2. Piccardi, Carlo & Calatroni, Lisa & Bertoni, Fabio, 2010. "Communities in Italian corporate networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(22), pages 5247-5258.
    3. Lou, Hao & Li, Shenghong & Zhao, Yuxin, 2013. "Detecting community structure using label propagation with weighted coherent neighborhood propinquity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(14), pages 3095-3105.

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