Finding "true" clusters in a data set is a challenging problem. Clustering solutions obtained using different models and algorithms do not necessarily provide compact and well-separated clusters or the optimal number of clusters. Cluster validity indices are commonly applied to identify such clusters. Nevertheless, these indices are typically relative, and they are used to compare clustering algorithms or choose the parameters of a clustering algorithm. Moreover, the success of these indices depends on the underlying data structure. This paper introduces novel absolute cluster indices to determine both the compactness and separability of clusters. We define a compactness function for each cluster and a set of neighboring points for cluster pairs. This function is utilized to determine the compactness of each cluster and the whole cluster distribution. The set of neighboring points is used to define the margin between clusters and the overall distribution margin. The proposed compactness and separability indices are applied to identify the true number of clusters. Using a number of synthetic and real-world data sets, we demonstrate the performance of these new indices and compare them with other widely-used cluster validity indices.

翻译：在数据集中发现“真实”聚类是一个具有挑战性的问题。使用不同模型和算法获得的聚类解未必能提供紧凑且分离良好的聚类或最优的聚类数量。聚类有效性指标通常被用于识别此类聚类。然而，这些指标通常是相对的，主要用于比较聚类算法或选择聚类算法的参数。此外，这些指标的成功与否取决于底层数据结构。本文提出了新颖的绝对聚类指标，用于同时确定聚类的紧密度和分离度。我们为每个聚类定义了一个紧密度函数，并为聚类对定义了一组邻近点。该函数用于确定每个聚类及整个聚类分布的紧密度。邻近点集用于定义聚类间的边界以及整体分布边界。所提出的紧密度和分离度指标被用于识别真实聚类数量。通过使用多个合成数据集和真实数据集，我们验证了这些新指标的性能，并将其与其他广泛使用的聚类有效性指标进行了比较。