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Information Theory in Scientific Visualization
Entropy 2011, 13(2), 450-465; doi:10.3390/e13020450
Article

Information Theoretic Hierarchical Clustering

1,2
, 1,3,4,*  and 1,4
1 Control and Intelligent Processing Center of Excellence, School of Electrical and Computer Engineering, University of Tehran, PO Box 1439957131, Tehran 14395-515, Iran 2 Department of Electrical and Computer Engineering, Michigan State University, East Lansing, MI 48824, USA 3 Radiology Image Analysis Laboratory, Henry Ford Health System, Detroit, MI 48202, USA 4 School of Cognitive Sciences, Institute for Research in Fundamental Sciences (IPM), PO Box 1954856316, Tehran, Iran
* Author to whom correspondence should be addressed.
Received: 8 December 2010 / Revised: 31 December 2010 / Accepted: 27 January 2011 / Published: 10 February 2011
(This article belongs to the Special Issue Advances in Information Theory)
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Abstract

Hierarchical clustering has been extensively used in practice, where clusters can be assigned and analyzed simultaneously, especially when estimating the number of clusters is challenging. However, due to the conventional proximity measures recruited in these algorithms, they are only capable of detecting mass-shape clusters and encounter problems in identifying complex data structures. Here, we introduce two bottom-up hierarchical approaches that exploit an information theoretic proximity measure to explore the nonlinear boundaries between clusters and extract data structures further than the second order statistics. Experimental results on both artificial and real datasets demonstrate the superiority of the proposed algorithm compared to conventional and information theoretic clustering algorithms reported in the literature, especially in detecting the true number of clusters.
Keywords: information theory; Rényi’s entropy; quadratic mutual information; hierarchical clustering; proximity measure information theory; Rényi’s entropy; quadratic mutual information; hierarchical clustering; proximity measure
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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MDPI and ACS Style

Aghagolzadeh, M.; Soltanian-Zadeh, H.; Araabi, B.N. Information Theoretic Hierarchical Clustering. Entropy 2011, 13, 450-465.

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