On kernel fuzzy c-means for data with tolerance using explicit mapping for kernel data analysis

An explicit mapping is generally unknown for kernel data analysis but their inner product should be known. Though kernel fuzzy c-means algorithm for data with tolerance has been proposed by the authors, the cluster centers and the tolerance in higher dimensional space have been unseen. Contrary to this common assumption, an explicit mapping has been introduced by one of the authors and the situation of kernel fuzzy c-means in higher dimensional space has been described via kernel principal component analysis using the explicit mapping. In this paper, the cluster centers and the tolerance of kernel fuzzy c-means for data with tolerance are described via kernel principal component analysis using the explicit mapping.