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Multiple Clustering Solutions Analysis through Least-Squares Consensus Algorithms

机译：最小二乘共识算法的多聚类解决方案分析

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摘要

Clustering is one of the most important unsupervised learning problems and it deals with finding a structure in a collection of unla-beled data; however, different clustering algorithms applied to the same data-set produce different solutions. In many applications the problem of multiple solutions becomes crucial and providing a limited group of good clusterings is often more desirable than a single solution. In this work we propose the Least Square Consensus clustering that allows a user to extrapolate a small number of different clustering solutions from an initial (large) set of solutions obtained by applying any clustering algorithm to a given data-set. Two different implementations are presented. In both cases, each consensus is accomplished with a measure of quality defined in terms of Least Square error and a graphical visualization is provided in order to make immediately interpretable the result. Numerical experiments are carried out on both synthetic and real data-sets.
机译：聚类是最重要的无监督学习问题之一，它涉及在无条件数据集合中查找结构。但是，应用于同一数据集的不同聚类算法会产生不同的解决方案。在许多应用中，多个解决方案的问题变得至关重要，与单个解决方案相比，通常更需要提供一组有限的良好聚类。在这项工作中，我们提出了最小二乘共识聚类，它允许用户从通过将任何聚类算法应用于给定数据集而获得的初始（大）解集中推断出少量不同的聚类解。介绍了两种不同的实现。在这两种情况下，每个共识都是通过用最小二乘误差定义的质量度量来实现的，并提供图形化可视化效果以使结果立即可解释。在合成和真实数据集上都进行了数值实验。

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