Research of space distortion in cluster analysis

我们研究了凝聚层次聚类算法在空间失真和单调性方面的可接受性，分别由Yadohisa，Takeuchi和Inada（1999）和Batagelj（1981）定义。Fisher和货车Ness（1971）提出了一种新的聚类算法的容许性，称为良结构容许性。Takeuchi，Yadohisa和Inada（2000）提出了一个衡量聚类结果的标准，称为“结构比”。它包含了良好结构的概念作为一种特殊情况，并代表了某种良好的聚类结果。然而，这些措施的特点（如这些措施和分散的对象之间的关系）仍然有待完成。在本研究中，我们还调查了结构化比率与分析数据之间的关系。

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.