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A new multiobjective clustering technique based on the concepts of stability and symmetry

机译：基于稳定性和对称性概念的多目标聚类新技术

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摘要

Most clustering algorithms operate by optimizing (either implicitly or explicitly) a single measure of cluster solution quality. Such methods may perform well on some data sets but lack robustness with respect to variations in cluster shape, proximity, evenness and so forth. In this paper, we have proposed a multiobjective clustering technique which optimizes simultaneously two objectives, one reflecting the total cluster symmetry and the other reflecting the stability of the obtained partitions over different bootstrap samples of the data set. The proposed algorithm uses a recently developed simulated annealing-based multiobjective optimization technique, named AMOSA, as the underlying optimization strategy. Here, points are assigned to different clusters based on a newly defined point symmetry-based distance rather than the Euclidean distance. Results on several artificial and real-life data sets in comparison with another multiobjective clustering technique, MOCK, three single objective genetic algorithm-based automatic clustering techniques, VGAPS clustering, GCUK clustering and HNGA clustering, and several hybrid methods of determining the appropriate number of clusters from data sets show that the proposed technique is well suited to detect automatically the appropriate number of clusters as well as the appropriate partitioning from data sets having point symmetric clusters. The performance of AMOSA as the underlying optimization technique in the proposed clustering algorithm is also compared with PESA-II, another evolutionary multiobjective optimization technique.
机译：大多数群集算法通过优化（隐式或显式）群集解决方案质量的单个度量来运行。这样的方法在某些数据集上可能表现良好，但是在群集形状，邻近度，均匀性等方面的变化方面缺乏鲁棒性。在本文中，我们提出了一种多目标聚类技术，该技术同时优化了两个目标，一个反映了总的集群对称性，另一个反映了在数据集的不同引导样本上获得的分区的稳定性。所提出的算法使用了最近开发的基于模拟退火的多目标优化技术，称为AMOSA，作为基础优化策略。在这里，基于新定义的基于点对称性的距离而不是欧几里得距离，将点分配给不同的群集。与另一种多目标聚类技术MOCK，三种基于单目标遗传算法的自动聚类技术，VGAPS聚类，GCUK聚类和HNGA聚类以及确定适当数量的杂合方法的几种混合方法相比，在多个人工和现实数据集上的结果来自数据集的聚类表明，提出的技术非常适合于自动检测具有点对称聚类的数据集的适当数量的聚类以及适当的分区。还将所提出的聚类算法中作为基础优化技术的AMOSA的性能与另一种进化型多目标优化技术PESA-II进行了比较。

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