Abstract
This paper proposes two types of kernel fuzzy c-means algorithms with an indefinite kernel. Both algorithms are based on the fact that the relational fuzzy c-means algorithm is a special case of the kernel fuzzy c-means algorithm. The first proposed algorithm adaptively updated the indefinite kernel matrix such that the dissimilarity between each datum and each cluster center in the feature space is non-negative, instead of subtracting the minimal eigenvalue of the given kernel matrix as its preprocess. This derivation follows the manner in which the non-Euclidean relational fuzzy c-means algorithm is derived from the original relational fuzzy c-means one. The second proposed method produces the memberships by solving the optimization problem in which the constraint of non-negative memberships is added to the one of K-sFCM. This derivation follows the manner in which the non-Euclidean fuzzy relational clustering algorithm is derived from the original relational fuzzy c-means one. Through a numerical example, the proposed algorithms are discussed.
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Kanzawa, Y., Endo, Y., Miyamoto, S. (2010). Indefinite Kernel Fuzzy c-Means Clustering Algorithms. In: Torra, V., Narukawa, Y., Daumas, M. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2010. Lecture Notes in Computer Science(), vol 6408. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16292-3_13
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DOI: https://doi.org/10.1007/978-3-642-16292-3_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-16291-6
Online ISBN: 978-3-642-16292-3
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