Mathematical Sciences: General Global Criteria for SelectingClustering Algorithms

该项目将开发使用Fisher和Van Ness的可接受聚类方法选择聚类程序的全球标准，并扩展了可接受条件的定义。这些容许条件将被应用于Lance和Williams提出的一般无限参数化聚类过程族；对于每种情况，将确定产生可接受算法的族参数空间的相应子集。聚类是一种常用的工具，用于将一组对象划分为子组或种类。它被分类学家、图书管理员、流行病学家、银行家、科学家和其他许多人用来将大型、复杂的对象集合分类为可以更好地理解和处理的同质组。多年来，已经提出了许多聚类方法，每种方法都给出了不同的聚类；因此，算法的选择很重要。这里的工作是根据特定应用程序所需的属性编写各种算法。

This project will develop global criteria for selecting clustering procedures using the admissible clustering approach of Fisher and Van Ness with extended definitions of admissibility conditions. These admissibility conditions will be applied to the general infinite parameterized family of clustering procedures proposed by Lance and Williams; and for each condition, the corresponding subset of the family's parameter space yielding admissible algorithms will be determined. Clustering is a heavily used tool for partitioning a group of objects into subgroups or species. It is used by taxonomists, librarians, epidemiologists, bankers, scientists and many others to classify large, complex sets of objects into homogeneous groups which can be comprehended and handled better. Numerous clustering methods have been proposed over the years, with each giving a different clustering; hence, the choice of algorithm is important. The work here is to codify the various algorithms according to the properties needed for a specific application.