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Kleinberg, J. (2003) An Impossibility Theorem for Clustering. Advances in Neural Information Processing Systems (NIPS 2002), 15, 463-470.

has been cited by the following article:

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

    AUTHORS: Kajsa Møllersen, Subhra S. Dhar, Fred Godtliebsen

    KEYWORDS: Background Noise, Gaussian Mixture Distribution, Kullback-Leibler, Outliers, Subcluster Weight

    JOURNAL NAME: Applied Mathematics, Vol.7 No.15, September 12, 2016

    ABSTRACT: 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.