Non-Euclidean Extension of FCMdd-Based Linear Clustering for Relational Data

Relational data is common in many real-world applications. Linear fuzzy clustering models have been extended for handling relational data based on Fuzzy c-Medoids (FCMdd) framework. In this paper, with the goal being to handle non-Euclidean data, beta-spread transformation of relational data matrices used in Non-Euclidean-type Relational Fuzzy (NERF) c-means is applied before FCMdd-type linear cluster extraction. beta-spread transformation modifies data elements to avoid negative values for clustering criteria of distances between objects and linear prototypes. In numerical experiments, typical features of the proposed approach are demonstrated not only using artificially generated data but also in a document classification task with a document-keyword co-occurrence relation.