Local subspace learning by extended fuzzy c-medoids clustering

Abstract

Linear fuzzy clustering is a technique for extracting linear-shape clusters, in which the fuzzy c-means (FCM)-like iterative procedure is performed with the prototypes of linear varieties, and is also regarded as a local subspace learning method. In fuzzy c-medoids (FCMdd), cluster prototypes are selected from data samples and clustering criteria are calculated by using only mutual distances among samples. Then, it is applicable to relational data clustering. This paper proposes an extended FCMdd approach for linear fuzzy clustering of relational data, which uses multiple representative objects (medoids) for representing prototypes. In the algorithm, new prototype is given by solving a combinatorial optimisation problem for searching medoids and the computational complexity is reduced by searching only from a subset of objects having large membership values. The information summarisation approach can be regarded as a multicluster-type multidimensional scaling for summarising data in multiple low-dimensional feature spaces.