Refining Fuzzy c-Means Membership Functions to Assimilate A Priori Knowledge of Cluster Sizes
Jiarui Li, Yukio Horiguchi, Tetsuo Sawaragi · 2018
Because Fuzzy C-Means (FCM) uses a sum-of-squared-errors objective function, it tends to equalize cluster populations, causing drifts of centers of smaller clusters to larger adjacent clusters. As a priori knowledge for clustering, the proportions of individual cluster sizes could well be available depending on application domains, on the other hand. The present paper proposes a method that can assimilate this information into the cluster structure by refining membership functions obtained by FCM. The proposed method, limited to one-dimensional fuzzy sets, modifies the position and shape of each cluster by the two-stage adjustment of its membership curve points towards the given proportions of cluster sizes. A numerical experiment was conducted to confirm the effectiveness of the proposed method, demonstrating that assimilating a priori knowledge of cluster sizes can contribute much to the accurate extraction of the original data structure.