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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.

62H30 Classification and discrimination; cluster analysis (statistical aspects)
62H86 Multivariate analysis and fuzziness
Full Text: DOI
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