Linear fuzzy clustering of relational data based on extended Fuzzy c-Medoids

Linear fuzzy clustering is a fuzzy clustering-based local PCA technique, in which the Fuzzy c-Means (FCM)-like iterative procedure is performed by using linear varieties as the prototypes of clusters. Fuzzy c-Medoids (FCMdd) is a modified FCM algorithm, in which the representative objects ldquomedoidsrdquo are selected from data samples, and is useful for handling relational data. This paper proposes an extended linear fuzzy clustering algorithm that can capture local linear sub-structures in relational data by estimating linear prototypes spanned by representative objects ldquomedoidsrdquo In the proposed algorithm, the clustering criterion is calculated using only the mutual distances among objects under the assumption of metric relational data, then estimation of linear prototypes is reduced to combinatorial optimization problems. In order to decrease the complexity of the prototype estimation step, a modified algorithm is also considered, in which the ldquomedoidsrdquo are selected only from a subset of objects having large membership values. The clustering result of the proposed method is also comparative with multi-dimensional scaling and characteristic features are demonstrated in numerical experiments.