Noise Rejection Approaches for Various Rough Set-Based C-Means Clustering
Seiki Ubukata, Sho Sekiya, Akira Notsu, and Katsuhiro Honda
Osaka Prefecture University
1-1 Gakuen-cho, Nakaku, Sakai, Osaka 599-8531, Japan
In the field of cluster analysis, rough set-based extensions of hard C-means (HCM; k-means) including rough C-means (RCM), rough set C-means (RSCM), and rough membership C-means (RMCM) are promising approaches for dealing with the certainty, possibility, uncertainty of belonging of object to clusters. Since C-means-type methods are strongly affected by noise, noise clustering approaches have been proposed. In noise clustering approaches, noise objects, which are far from any cluster center, are rejected for robust estimation. In this paper, we introduce noise rejection approaches for rough set-based C-means based on probabilistic memberships and propose noise RCM with membership normalization (NRCM-MN), noise RSCM with membership normalization (NRSCM-MN), and noise RMCM (NRMCM). In addition, visualization demonstration of the cluster boundaries on the two-dimensional plane of the proposed methods is carried out to confirm the characteristics of each method. Furthermore, the clustering performance is verified by numerical experiments using real-world datasets.
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