An Algorithm for the Separation-Preserving Transition of Clusterings

S. Borgwardt, Felix Happach, Stetson Zirkelbach
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引用次数: 1

Abstract

The separability of clusters is one of the most desired properties in clustering. There is a wide range of settings in which different clusterings of the same data set appear. We are interested in applications for which there is a need for an explicit, gradual transition of one separable clustering into another one. This transition should be a sequence of simple, natural steps that upholds separability of the clusters throughout. We design an algorithm for such a transition. We exploit the intimate connection of separability and linear programming over bounded-shape partition and transportation polytopes: separable clusterings lie on the boundary of partition polytopes and form a subset of the vertices of the corresponding transportation polytopes, and circuits of both polytopes are readily interpreted as sequential or cyclical exchanges of items between clusters. This allows for a natural approach to achieve the desired transition through a combination of two walks: an edge walk between two so-called radial clusterings in a transportation polytope, computed through an adaptation of classical tools of sensitivity analysis and parametric programming, and a walk from a separable clustering to a corresponding radial clustering, computed through a tailored, iterative routine updating cluster sizes and reoptimizing the cluster assignment of items.
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一种保持分离的聚类转移算法
聚类的可分性是聚类中最理想的性质之一。存在多种设置,其中会出现同一数据集的不同聚类。我们感兴趣的是需要从一个可分离的集群显式、渐进地过渡到另一个集群的应用。这种转变应该是一系列简单、自然的步骤,在整个过程中维护集群的可分离性。我们为这种转换设计了一个算法。我们利用有界形状划分和运输多面体上的可分性和线性规划的密切联系:可分离的簇位于划分多面体的边界上,并形成相应运输多面体的顶点的子集,两个多面体的回路很容易被解释为簇之间项目的顺序或循环交换。这允许一种自然的方法通过两种走线的组合来实现所需的过渡:通过适应灵敏度分析和参数编程的经典工具计算的运输多面体中两个所谓径向聚类之间的边走线,以及通过定制的,迭代例程更新集群大小并重新优化项目的集群分配。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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