Relational Fuzzy c-Means and Kernel Fuzzy c-Means Using an Object-Wise β-Spread Transformation
Shibaura Institute of Technology, 3-7-5 Toyosu, Koto, Tokyo 135-8548, Japan
Clustering methods of relational data are often based on the assumption that a given set of relational data is Euclidean, and kernelized clustering methods are often based on the assumption that a given kernel is positive semidefinite. In practice, non-Euclidean relational data and an indefinite kernel may arise, and a β-spread transformation was proposed for such cases, which modified a given set of relational data or a give a kernel Gram matrix such that the modified β value is common to all objects. In this paper, we propose an object-wise β-spread transformation for use in both relational and kernelized fuzzy c-means clustering. The proposed system retains the given data better than conventional methods, and numerical examples show that our method is efficient for both relational and kernel fuzzy c-means.
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