Agglomerative Hierarchical Clustering   Without Reversals on Dendrograms Using Asymmetric Similarity Measures

Satoshi Takumi; Sadaaki Miyamoto

doi:10.20965/jaciii.2012.p0807

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JACIII Vol.16 No.7 pp. 807-813

doi: 10.20965/jaciii.2012.p0807

(2012)

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Agglomerative Hierarchical Clustering Without Reversals on Dendrograms Using Asymmetric Similarity Measures

Satoshi Takumi and Sadaaki Miyamoto

Department of Risk Engineering, School of Systems and Information Engineering, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8577, Japan

Received:

November 29, 2011

Accepted:

September 25, 2012

Published:

November 20, 2012

Keywords:

agglomerative clustering, asymmetric similarity, asymmetric dendrogram

Abstract

Algorithms of agglomerative hierarchical clustering using asymmetric similarity measures are studied. Two different measures between two clusters are proposed, one of which generalizes the average linkage for symmetric similarity measures. Asymmetric dendrogram representation is considered after foregoing studies. It is proved that the proposed linkage methods for asymmetric measures have no reversals in the dendrograms. Examples based on real data show how the methods work.

Cite this article as:

S. Takumi and S. Miyamoto, “Agglomerative Hierarchical Clustering Without Reversals on Dendrograms Using Asymmetric Similarity Measures,” J. Adv. Comput. Intell. Intell. Inform., Vol.16, No.7, pp. 807-813, 2012.

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References

[1] M. R. Anderberg, “Cluster Analysis for Applications,” Academic Press, New York, 1960.
[2] B. S. Everitt, “Cluster Analysis, 3rd Edition,” Arnold, London, 1993.
[3] L. Hubert, “Min and max hierarchical clustering using asymmetric similarity measures,” Psychometrika, Vol.38, No.1, pp. 63-72, 1973.
[4] A. Okada and T. Iwamoto, “A Comparison before and after the Joint First Stage Achievement Test by Asymmetric Cluster Analysis,” Behaviormetrika, Vol.23, No.2, pp. 169-185, 1996.
[5] H. Yadohisa, “Formulation of Asymmetric Agglomerative Clustering and Graphical Representation of Its Result,” J. of Japanese Society of Computational Statistics, Vol.15, No.2, pp. 309-316, 2002 (in Japanese).
[6] S. Miyamoto, “Fuzzy Sets in Information Retrieval and Cluster Analysis,” Kluwer, Dordrecht, 1990.
[7] S. Miyamoto, “Introduction to Cluster Analysis,” Morikita-Shuppan, Tokyo, 1999 (in Japanese).
[8] T. Saito and H. Yadohisa, “Data Analysis of Asymmetric Structures,” Marcel Dekker, New York, 2005.
[9] A. Takeuchi, T. Saito, and H. Yadohisa, “Asymmetric agglomerative hierarchical clustering algorithms and their evaluations,” J. of Classification, Vol.24, pp. 123-143, 2007.
[10] S. M. “Stigler, Citation Patterns in the Journals of Statistics and Probability,” Statistical Science, Vol.9, pp. 94-108, 1994.
[11] http://www.jetro.go.jp/indexj.html
[12] http://www.stat.go.jp/index.htm

This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.

[1] [1] M. R. Anderberg, “Cluster Analysis for Applications,” Academic Press, New York, 1960.

[2] [2] B. S. Everitt, “Cluster Analysis, 3rd Edition,” Arnold, London, 1993.

[3] [3] L. Hubert, “Min and max hierarchical clustering using asymmetric similarity measures,” Psychometrika, Vol.38, No.1, pp. 63-72, 1973.

[4] [4] A. Okada and T. Iwamoto, “A Comparison before and after the Joint First Stage Achievement Test by Asymmetric Cluster Analysis,” Behaviormetrika, Vol.23, No.2, pp. 169-185, 1996.

[5] [5] H. Yadohisa, “Formulation of Asymmetric Agglomerative Clustering and Graphical Representation of Its Result,” J. of Japanese Society of Computational Statistics, Vol.15, No.2, pp. 309-316, 2002 (in Japanese).

[6] [6] S. Miyamoto, “Fuzzy Sets in Information Retrieval and Cluster Analysis,” Kluwer, Dordrecht, 1990.

[7] [7] S. Miyamoto, “Introduction to Cluster Analysis,” Morikita-Shuppan, Tokyo, 1999 (in Japanese).

[8] [8] T. Saito and H. Yadohisa, “Data Analysis of Asymmetric Structures,” Marcel Dekker, New York, 2005.

[9] [9] A. Takeuchi, T. Saito, and H. Yadohisa, “Asymmetric agglomerative hierarchical clustering algorithms and their evaluations,” J. of Classification, Vol.24, pp. 123-143, 2007.

[10] [10] S. M. “Stigler, Citation Patterns in the Journals of Statistics and Probability,” Statistical Science, Vol.9, pp. 94-108, 1994.

[11] [11] http://www.jetro.go.jp/indexj.html

[12] [12] http://www.stat.go.jp/index.htm