Fuzzy-Enhanced Analysis of Streaming Clustering: Exploring Drift and Growth of Clusters

In this paper, we introduce four novel measures designed to assess the growth and drift of clusters in the context of streaming data analysis: Local Incremental Drift (LID), Global Incremental Drift (GID), Local Incremental Growth (LIG), and Global Incremental Growth (GIG). These measures address the limitation of existing incremental cluster validity indices (iCVIs) which require at least two clusters, and they offer a comprehensive framework for monitoring each evolving structure in the dynamic realm of online streaming clustering. Through experiments involving synthetic and real-life streaming datasets, we investigated how the proposed measures can be used to observe and analyze the performance of the University of Missouri Streaming Clustering (MUSC) algorithm. We also mapped the raw values of the measures into appropriate fuzzy membership functions for corresponding fuzzy concepts. Our experiments show that these measures effectively capture the trends of growth and drift for Gaussian clusters. In addition to the change in size and location of evolving structures, the measures can also provide other information about the streaming process such as the time a new structure appears and stabilizes, effect of different streaming sample order, etc.