A Note on Fuzzy Joint Points Clustering Methods for Large Datasets

Integrating clustering algorithms with fuzzy logic typically yields more robust methods, which require little to no supervision of user. The fuzzy joint points method is a density-based fuzzy clustering approach that can achieve quality clustering. However, early versions of the method hold high computational complexity. In a recent work, the speed of the method was significantly improved without sacrificing clustering efficiency, and an even faster but parameter-dependent method was also suggested. Yet, the clustering performance of the latter was left as an open discussion and subject of study. In this study, we prove the existence of the appropriate parameter value and give an upper bound on it to discuss whether and how the parameter-dependent method can achieve the same clustering performance with the original method.