Abstract
Handling relational data is an active topic in fuzzy clustering. In our previous work, we proposed an extended version of linear fuzzy clustering based on Fuzzy c-Medoids (FCMdd), which is used with non-Euclidean relational data. In order to handle non-Euclidean data, beta-spread transformation of relational data matrices used in NERF (non-Euclidean-type Fuzzy c-Means) was applied before FCMdd-type linear cluster extraction. In this paper, the linear fuzzy clustering model is further improved so that the beta-spread transformation is automatically achieved by avoiding negative values for clustering criteria of distances between objects and linear prototypes. In a graded approach, the shift value in spreading transformation is gradually increased considering triangle inequalities among distance measures.
