Weighted fuzzy clustering on subsets of variables

A fuzzy clustering method considering weights of variable-based dissimilarities over objects in the subspace of the objectpsilas space is proposed. In order to estimate the weights, we propose two methods. One is a method in which a conventional fuzzy clustering method is directly used for the variable-based dissimilarity data. The other is to use a new objective function. Exploiting the weights, we define a dissimilarity assigned with the significance of each variable for the classification and reduce the number of variables. We can implement a fuzzy clustering method under the intrinsically weighted classification structure on the subspace of data. Several numerical examples show the improved performance and the applicability of our proposed method.