Novel validity indices for dynamic clustering and an Improved Dynamic Fuzzy C-Means

Dynamic clustering algorithms play a crucial role in numerous real-world applications by continuously adapting to evolving data patterns and identifying changes within the underlying cluster structure. However, unlike static clustering, where a plethora of validation indices exist to assess the solution's quality, evaluating the effectiveness of dynamic clustering algorithms remains a challenge. This paper addresses this gap by proposing a novel set of six validation indices specifically designed for dynamic clustering. These indices assess the quality of solutions generated at three distinct granularities: individual clusters, individual observation periods, and the entire observation horizon. Our focus centers on cluster creation and elimination, recognized as the most critical structural changes within the dynamic clustering literature. To illustrate the application of these novel indices, we introduce an improved version of the dynamic fuzzy c-means algorithm (I-DFCM) which offers enhanced computational stability for handling dynamic data. We demonstrate the effectiveness of both the IDFCM algorithm and the new validation indices through computational experiments using both synthetic and real-world datasets. The experiments showcase how these indices can effectively validate dynamic clustering solutions and guide parameter tuning for optimal performance, and support practical applications such as dynamic community detection in social networks and informed decision-making in dynamic environments. The results highlight the significant potential of these new validation indices and the I-DFCM algorithm in advancing the field of dynamic clustering.