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Soft clustering

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Abstract Clustering is one of the most used tools in data analysis. In the last decades, due to the increasing complexity of data, soft clustering has received a great deal of attention. There exist different approaches that can be considered as soft. The most known is the fuzzy approach that consists in assigning objects to clusters with membership degrees, depending on the dissimilarities between each object and all the prototypes, ranging in the unit interval. Closely related to the fuzzy approach, there is the possibilistic one that, differently from the previous one, relaxes some constraints on the membership degrees. In particular, the objects are assigned to clusters with degrees of typicalities, depending just on the dissimilarities between each object and the closest prototype. A further soft approach is the rough one. In this case, there are not degrees ranging between 0 and 1 but objects with intermediate features belong to the boundary region and are assigned to more than one cluster. Even if it is not universally recognized in the scientific community as an approach of soft clustering, from our point of view, the model‐based approach can also be considered as such. Model‐based clustering methods also produce a soft partition of the objects and the posterior probability of a component membership may play a role similar to the membership degree. The four approaches are critically described from a theoretical point of view and an empirical comparative analysis is carried out. This article is categorized under: Statistical Learning and Exploratory Methods of the Data Sciences > Clustering and Classification Statistical and Graphical Methods of Data Analysis > Multivariate Analysis Statistical Learning and Exploratory Methods of the Data Sciences > Exploratory Data Analysis
Scatter plot of the “DemoData2C2Da” dataset
[ Normal View | Magnified View ]
Partitions obtained by the four methods. Blue points indicate Cluster 1, green points indicate Cluster 2 and yellow points denote objects with membership degrees lower than 0.7 for FkM, objects with typicality values lower than 0.5 for PkM, objects in both the upper approximations for RkM and objects with posterior probabilities lower than 0.7 for FMG
[ Normal View | Magnified View ]

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Statistical Learning and Exploratory Methods of the Data Sciences > Clustering and Classification
Statistical Learning and Exploratory Methods of the Data Sciences > Exploratory Data Analysis
Statistical and Graphical Methods of Data Analysis > Multivariate Analysis

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