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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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