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Towards a robust fuzzy clustering. (English) Zbl 1043.62058
Summary: Fuzzy clustering helps to find natural vague boundaries in data. The Fuzzy \(C\)-Means method (FCM) is one of the most popular clustering methods based on minimization of a criterion function. However, one of the greatest disadvantages of this method is its sensitivity to presence of noise and outliers in data.
This paper introduces a new \(\varepsilon\)-insensitive Fuzzy \(C\)-Means (\(\varepsilon\)FCM) clustering algorithm. As a special case, this algorithm includes the well-known Fuzzy \(C\)-Medians method (FCMED). Also, methods with insensitivity control named \(\alpha\)FCM and \(\beta\)FCM are introduced. Performance of the new clustering algorithm is experimentally compared with the FCM method using synthetic data with outliers and heavy-tailed and overlapped groups of data in background noise.

MSC:
62H30 Classification and discrimination; cluster analysis (statistical aspects)
91C20 Clustering in the social and behavioral sciences
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