Effects of Semi-supervised Learning on Rough Membership C- Means Clustering

Rough C-means (RCM), rough set C-means (RSCM), and rough membership C-means (RMCM) are extensions of hard C-means (HCM) clustering based on rough set theory, and can deal with positive, possible, and uncertain belonging of objects to clusters. RSCM and RMCM are clustering models on the approximation space granulated by a binary relation, and the granularity of the object space is considered. Rough membership is the conditional probability of a cluster in the neighborhood of an object, and is useful as a probabilistic cluster membership. For RCM and RSCM, the usefulness of semi-supervised learning, in which partial labeled objects are used as supervision, has been reported. In this study, we propose semi-supervised RMCM methods and verify their effects by numerical experiments.