Abstract
Fuzzy c-Medoids (FCMdd) is a modified version of Fuzzy c-Means (FCM), in which the prototypes of clusters are selected from data samples, and is easily applied to relational data. This paper proposes a linear fuzzy clustering algorithm based on extended FCMdd in order to extract local sub-structures from relational data by estimating linear prototypes spanned by representative objects (medoids). While the prototype estimation phase is reduced to a combinatorial optimization problem, a linearized algorithm is also considered, in which the representative objects of “medoids” are selected only from a subset of objects having large membership values. The clustering result of the proposed method is also useful for low-dimensional visualization of relational data by estimating multiple 1-D plots even when multi-dimensional scaling fails to construct a meaningful single low-dimensional feature space.
