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On Data-Independent Properties for Density-Based Dissimilarity Measures in Hybrid Clustering

Permanent lenke
https://hdl.handle.net/10037/10769
DOI
https://doi.org/10.4236/am.2016.715143
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article.pdf (3.897Mb)
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Dato
2016-09-12
Type
Journal article
Tidsskriftartikkel
Peer reviewed

Forfatter
Møllersen, Kajsa; Dhar, Subhra; Godtliebsen, Fred
Sammendrag
Hybrid clustering combines partitional and hierarchical clustering for computational effectiveness and versatility in cluster shape. In such clustering, a dissimilarity measure plays a crucial role in the hierarchical merging. The dissimilarity measure has great impact on the final clustering, and data-independent properties are needed to choose the right dissimilarity measure for the problem at hand. Properties for distance- based dissimilarity measures have been studied for decades, but properties for density-based dissimilarity measures have so far received little attention. Here, we propose six data-independent properties to evaluate density-based dissimilarity measures associated with hybrid clustering, regarding equality, orthogonality, symmetry, outlier and noise observations, and light-tailed models for heavy-tailed clusters. The significance of the properties is investigated, and we study some well-known dissimilarity measures based on Shannon entropy, misclassification rate, Bhattacharyya distance and Kullback-Leibler divergence with respect to the proposed properties. As none of them satisfy all the proposed properties, we introduce a new dissimilarity measure based on the Kullback-Leibler information and show that it satisfies all proposed properties. The effect of the proposed properties is also illustrated on several real and simulated data sets.
Beskrivelse
Source: doi: 10.4236/am.2016.715143
Forlag
Scientific Research Publishing
Sitering
Møllersen, K., Dhar, S.S. and Godtliebsen, F. (2016) On Data-Independent Properties for Density-Based Dissimilarity Measures in Hybrid Clustering. Applied Mathematics , 7, 1674-1706. http://dx.doi.org/10.4236/am.2016.715143
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