SIAM Journal on Discrete Mathematics, Volume 35, Issue 1, Page 152-178, January 2021.
Clustering is one of the fundamental tasks in data analytics and machine learning. In many situations, different clusterings of the same data set become relevant. For example, different algorithms for the same clustering task may return dramatically different solutions. We are interested in applications in which one clustering has to be transformed into another, e.g., when a gradual transition from an old solution to a new one is required. In this paper, we devise methods for constructing such a transition based on linear programming and network theory. We use a so-called clustering-difference graph to model the desired transformation and provide methods for decomposing the graph into a sequence of elementary moves that accomplishes the transformation. These moves are equivalent to the edge directions, or circuits, of the underlying partition polytopes. Therefore, in addition to a conceptually new metric for measuring the distance between clusterings, we provide new bounds on the circuit diameter of these partition polytopes.

中文翻译：

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构建聚类转换

SIAM 离散数学杂志，第 35 卷，第 1 期，第 152-178 页，2021 年 1 月。
聚类是数据分析和机器学习的基本任务之一。在许多情况下，同一数据集的不同聚类变得相关。例如，同一聚类任务的不同算法可能会返回截然不同的解决方案。我们对需要将一个聚类转换为另一个聚类的应用感兴趣，例如，当需要从旧解决方案逐渐过渡到新解决方案时。在本文中，我们设计了基于线性规划和网络理论构建这种转换的方法。我们使用所谓的聚类差异图来模拟所需的转换，并提供将图分解为完成转换的基本移动序列的方法。这些移动相当于边缘方向，或电路，底层分区多胞体。因此，除了用于测量聚类之间距离的概念上的新度量外，我们还提供了这些分区多胞体的电路直径的新界限。