Abstract
Fuzzy c-means clustering is a useful method for capturing group-level heterogeneity of objects. This method estimates cluster centroids and fuzzy memberships simultaneously. A potential limitation of fuzzy c-means is that it may fail to detect clusters of different sizes. To address this difficulty, we propose an extension of FCM, called hierarchically structured FCM, which can detect clusters of different sizes as well as provide additional information on nested structures of clusters. Unlike extant hierarchical extensions of FCM that execute FCM at each level of hierarchy separately in a sequential manner, the proposed method estimates cluster centroids and fuzzy memberships in different levels simultaneously by minimizing a single objective function. The optimal number of clusters and sub-clusters is determined by examining cluster validity measures. The usefulness of the proposed method is illustrated by analyzing two synthetic data and real image data.
