Selecting the number of clusters is one of the key processes when applying clustering algorithms. To fulfill this task, various cluster validity indices (CVIs) have been introduced. Most of the cluster validity indices are defined to detect the optimal number of clusters hidden in a dataset. However, users sometimes do not expect to get the optimal number of groups but a secondary one which is more reasonable for their applications. This has motivated us to introduce a Bayesian cluster validity index (BCVI) based on existing underlying indices. This index is defined based on either Dirichlet or Generalized Dirichlet priors which result in the same posterior distribution. Our BCVI is then tested based on the Wiroonsri index (WI), and the Wiroonsri-Preedasawakul index (WP) as underlying indices for hard and soft clustering, respectively. We compare their outcomes with the original underlying indices, as well as a few more existing CVIs including Davies and Bouldin (DB), Starczewski (STR), Xie and Beni (XB), and KWON2 indices. Our proposed BCVI clearly benefits the use of CVIs when experiences matter where users can specify their expected range of the final number of clusters. This aspect is emphasized by our experiment classified into three different cases. Finally, we present some applications to real-world datasets including MRI brain tumor images. Our tools will be added to a new version of the recently developed R package ``UniversalCVI''.

翻译：选择聚类数目是应用聚类算法时的关键步骤之一。为完成此任务，已提出了多种聚类有效性指标（CVIs）。通常，这些指标被设计用于检测数据集中隐藏的最佳聚类数目。然而，用户有时并不期望获得最优聚类数，而是希望得到一个更符合其应用场景的次优方案。这促使我们基于现有底层指标提出一种贝叶斯聚类有效性指标（BCVI）。该指标基于Dirichlet先验或广义Dirichlet先验定义，二者可产生相同的后验分布。我们以Wiroonsri指标（WI）和Wiroonsri-Preedasawakul指标（WP）作为底层指标，分别针对硬聚类和软聚类测试所提出的BCVI，并将其结果与原始底层指标及Davies与Bouldin（DB）、Starczewski（STR）、Xie与Beni（XB）以及KWON2等现有指标进行对比。当用户可通过经验指定最终聚类数的预期范围时，所提出的BCVI能显著提升CVIs的使用效果。这一点通过分为三种不同场景的实验得到验证。最后，我们展示了在真实世界数据集（包括MRI脑肿瘤图像）上的应用，相关工具将添加到最新开发的R包"UniversalCVI"的新版本中。