树状图族
Families of dendrograms
摘要：
通过描述n个数据点的所有树状图的空间，并使用Murtagh（2004 b）最近应用的方法将其与具有穿孔的p-adic黎曼球面的模空间相关联，从p-adic几何的观点引入聚类分析的概念框架。该方法将树状图作为子树嵌入到与p-adic数相关联的Bruhat-Tits树中，并追溯到Cornelissen等人（2001）在p-adic几何中。在解释了定义之后，在模空间的背景下讨论了分类器的概念，并给出了树状图中隐藏顶点数的上界。
英文摘要：
A conceptual framework for cluster analysis from the viewpoint of p-adic geometry is introduced by describing the space of all dendrograms for n datapoints and relating it to the moduli space of p-adic Riemannian spheres with punctures using a method recently applied by Murtagh (2004b). This method embeds a dendrogram as a subtree into the Bruhat-Tits tree associated to the p-adic numbers, and goes back to Cornelissen et al. (2001) in p-adic geometry. After explaining the definitions, the concept of classifiers is discussed in the context of moduli spaces, and upper bounds for the number of hidden vertices in dendrograms are given.
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