Research of space distortion in cluster analysis

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We made a study of the admissibility of agglomerative hierarchical clustering algorithms with respect to space distortion and monotonicity, as defined by Yadohisa, Takeuchi and Inada (1999) and Batagelj (1981), respectively. Several admissibilities and their properties were given for selecting a clustering algorithm.Fisher and Van Ness (1971) proposed a new admissibility of a clustering algorithm called well-structured admissible. Takeuchi, Yadohisa and Inada (2000) proposed a criterion for measuring the clustering result called "structure ratio". It includes the concept of well-structured as a special case, and represents some kind of goodness of the result of the clustering. However, the characterizations of these measures (e.g. the relationship between these measures and dispersion of objects) are still remained to be completed. In this research, we also investigated the relationship between the structured ratio and the data analyzed.