Agglomerative Hierarchical Clustering Using the Tθ Family of Similarity Measures

In this work, we begin with the presentation of the
Tθ family of usual similarity measures concerning multidimensional
binary data. Subsequently, some properties of these measures are
proposed. Finally the impact of the use of different inter-elements
measures on the results of the Agglomerative Hierarchical Clustering
Methods is studied.

• Salima Kouici
• Abdelkader Khelladi

• Binary data
• similarity measure
• Tθ measures
• Agglomerative Hierarchical Clustering.

[1] V. Bategelj and M. Bern, Comparing resemblance measures, Journal of
classification Vol.1 , pp.73-90, 1995.
[2] J. C. Gower and P. Legendre, A general coefficient of similarity and
some of its properties, Biometrics 27, pp. 857-871,1986.
[3] N. Jardine and R. Sibson, Mathematical Taxonomy, Wiley Ed., London,
1971.
[4] S. Kouici and A. Khelladi, Structurel similarity measure for binary
data clustering, Far east journal of applied mathematics Vol. 30 N2,
pp.189-202, 2008.
[5] M-J Lesot, M. Rifqi and H. Benhadda, Similarity measures for
binary and numerical data: a survey, International journal: Knowledge
Engineering and Soft Data Parardigms Vol.1 N1, pp.63-84, 2009.
[6] J.P. Nakache and J. Confais, Approche pragmatique de la classification,
Editions TECHNIP, Paris, 2005.
[7] J-F. Omhover, M. Rifqi and M. Detyniecki, Ranking Invariance
Based on Similarity Measures in Document Retrieval, Lecture Notes in
Computer Science, 2006, Volume 3877, Adaptive Multimedia Retrieval:
User, Context, and Feedback, pp. 55-64
[8] R.R Sokal and C.D. Michener, A Statistical Method for evaluating
systematics relationships, Univ. Kansas Sci. Bull.,38,pp.1409-1438, 1958.
[9] T. Sorensen, A Method of Establishing Groups of Equal Amplitude
in Plant Sociology Based on Similarities of species Content and its
Application to Analyses of the Vegetation on Danish Commons, Biologiske
Skrifter,5, pp 1-34, 1948.
[10] A. Tversky, Features of similarity, Psychological Review Vol.84,
pp.327-352, 1977.
[11] J.H. Ward, Hierarchical Grouping to Optimize an Objectif Function, J.
Am. Statisti. Assoc.,58,pp 236-244, 1963.