A Bayesian cluster validity index

Selecting the appropriate number of clusters is a critical step in applying clustering algorithms. To assist in this process, various cluster validity indices (CVIs) have been developed. These indices are designed to identify the optimal number of clusters within a dataset. However, users may not always seek the absolute optimal number of clusters but rather a secondary option that better aligns with their specific applications. This realization has led us to introduce a Bayesian cluster validity index (BCVI), which builds upon existing indices. The BCVI utilizes either Dirichlet or generalized Dirichlet priors, resulting in the same posterior distribution. We evaluate our BCVI using the Wiroonsri index for hard clustering and the Wiroonsri-Preedasawakul index for soft clustering as underlying indices. We compare the performance of our proposed BCVI with that of the original underlying indices and several other existing CVIs, including Davies-Bouldin, Starczewski, Xie-Beni, and KWON2 indices. Our BCVI offers clear advantages in situations where user expertise is valuable, allowing users to specify their desired range for the final number of clusters. To illustrate this, we conduct experiments classified into three different scenarios. Additionally, we showcase the practical applicability of our approach through real-world datasets, such as MRI brain tumor images. These tools will be published as a new R package 'BayesCVI'.