Research on the multilateral evaluation of the result of the cluster analysis

凝聚层次聚类算法是聚类分析中最常用的一系列算法的总称。由于凝聚层次聚类算法可以利用相似性来对对象进行分类，并且可以在树状图上直观地显示聚类的形成情况，因此易于解释，因此被广泛应用于许多领域。当数据对称时，我们提出了关注“空间失真”、“组合距离的单调性”、“衡量+聚类结果的结构化比率”的指标，并对聚类分析的结果进行了多边评价，结果公布为Akinobu Takeuchi，Hiroshi Yadohisa和Koichi Inada《凝聚层次聚类算法中分类结果的评价》(学会统计数学研究所项目研究(2004))。此外，结合本研究，我们研究了多元函数数据的CRISP和FUZZY k-均值聚类算法。

The agglomerative hierarchical clustering algorithms is a generic name of a series of talgorithms used best in the cluster analysis. It is easy to interpret because the agglomerative hierarchical clustering algorithms can classify the object by using a dissimilarity, and can show the formation situation of the clustering in the sight in the dendrogram and is used in a lot of fields. When the data is symmetric, we proposed the index that pays attention to "space distortion", "monotonicity of the combined distance", "Structured ratio for measuring the +clustering results", and the result of the cluster analysis has been evaluated multilaterally, The result is announced as Akinobu Takeuchi, Hiroshi Yadohisa and Koichi Inada "Evaluation of the classification result in the agglomerative hierarchical clustering algorithms" (the society by the project research of the Institute of Statistical Mathematics (2004)). Moreover, we investigated the crisp and fuzzy k-means clustering algorithms for multivariate functional data in association with this research.