Admissibilities of Agglomerative Hierarchical Clustering Algorithms with Respect to Space Distortion and Monotonicity
نویسندگان
چکیده
The concept of admissibility with respect to clustering algorithms was introduced by Fisher and Van Ness (1971). They defined types of admissibility of an algorithm and indicated the relationships between these admissibilities and popular clustering algorithms. In recent years, admissibility with respect to space distortion (See, Lance and Williams, 1967) has been proposed by Chen and Van Ness (1994 and 1996). Mirkin (1996) proposed the admissibility for monotonicity of an updating formula. In this paper, we propose new admissibilities with respect to space distortion and monotonicity, which are defined by Yadohisa, Takeuchi and Inada (1999) and Mirkin (1996), respectively. We also provide the necessary and sufficient conditions for Lance and Williams’ updating formula for the proposed admissibilities.
منابع مشابه
Space Distortion and Monotone Admissibility in Agglomerative Clustering
This paper discusses the admissibility of agglomerative hierarchical clustering algorithms with respect to space distortion and monotonicity, as defined by Yadohisa et al. and Batagelj, respectively. Several admissibilities and their properties are given for selecting a clustering algorithm. Necessary and sufficient conditions for an updating formula, as introduced by Lance and Williams, are pr...
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