  Cluster analysis is widely used in the areas of machine learning and data
mining. Fuzzy clustering is a particular method that considers that a data
point can belong to more than one cluster. Fuzzy clustering helps obtain
flexible clusters, as needed in such applications as text categorization. The
performance of a clustering algorithm critically depends on the number of
clusters, and estimating the optimal number of clusters is a challenging task.
Quality indices help estimate the optimal number of clusters. However, there is
no quality index that can obtain an accurate number of clusters for different
datasets. Thence, in this paper, we propose a new cluster quality index
associated with a visual, graph-based solution that helps choose the optimal
number of clusters in fuzzy partitions. Moreover, we validate our theoretical
results through extensive comparison experiments against state-of-the-art
quality indices on a variety of numerical real-world and artificial datasets.
