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Fuzzy $$c$$-ordered-means clustering. (English) Zbl 06840609
Summary: Fuzzy clustering helps to find natural vague boundaries in data. The fuzzy $$c$$-means method 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 the presence of noise and outliers in data. This paper introduces a new robust fuzzy clustering method named fuzzy $$C$$-ordered-means (FCOM) clustering. This method uses both the Huber’s M-estimators and the Yager’s OWA operators to obtain its robustness. The proposed method is compared to many other ones, e.g.: the fuzzy $$C$$-means (FCM), the possibilistic clustering (PC), the fuzzy noise clustering method (NCM), the $$L_p$$ norm clustering ($$L_p$$ FCM) ($$0 < p < 1$$), the $$L_1$$ norm clustering ($$L_1$$ FCM), the fuzzy clustering with polynomial fuzzifier (PFCM) and the $$\varepsilon$$-insensitive fuzzy $$C$$-means ($$\beta$$FCM). To this end, experiments on synthetic data with outliers are performed as well as on data with heavy-tailed and overlapping groups of points in background noise.

##### MSC:
 62H30 Classification and discrimination; cluster analysis (statistical aspects) 62H86 Multivariate analysis and fuzziness
robustbase
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