Conventional clustering algorithms classify a set of objects into some clusters with clear boundaries, that is, one object must belong to one cluster. However, many objects belong to more than one cluster in real world since the boundaries of clusters generally overlap with each other. Fuzzy-set representation of clusters makes it possible for each object to belong to more than one cluster. On the other hand, the fuzzy degree is sometimes regarded as too descriptive for interpreting clustering results. Rough-set representation could deal with such cases. Clustering based on rough set could provide a solution that is less restrictive than conventional clustering and less descriptive than fuzzy clustering. This paper proposes a rough clustering algorithm which is based on optimization of an objective function and the calculation formula of cluster centers is the same as one by Lingras et al. Moreover, it shows effectiveness of our proposed clustering algorithm in comparison with other algorithms. C 2013 Wiley Periodicals, Inc.
Conventional clustering algorithms classify a set of objects into some clusters with clear boundaries, that is, one object must belong to one cluster. However, many objects belong to more than one cluster in real world since the boundaries of clusters generally overlap with each other. Fuzzy‐set representation of clusters makes it possible for each object to belong to more than one cluster. On the other hand, the fuzzy degree is sometimes regarded as too descriptive for interpreting clustering results. Rough‐set representation could deal with such cases. Clustering based on rough set could provide a solution that is less restrictive than conventional clustering and less descriptive than fuzzy clustering. This paper proposes a rough clustering algorithm which is based on optimization of an objective function and the calculation formula of cluster centers is the same as one by Lingras et al. Moreover, it shows effectiveness of our proposed clustering algorithm in comparison with other algorithms.
A clustering method referred to as K-member clustering classifies a dataset into certain clusters, the size of which is more than a given constant K. Even-sized clustering, which classifies a dataset into even-sized clusters, is also considered along with K-member clustering. In our previous study, we proposed Even-sized Clustering Based on Optimization (ECBO) to output adequate results by formulating an even-sized clustering problem as linear programming. The simplex method is used to calculate the belongingness of each object to clusters in ECBO. In this study, ECBO is extended by introducing ideas that were introduced in K-means or fuzzy c-means to resolve problems of initial-value dependence, robustness against outliers, calculation costs, and nonlinear boundaries of clusters. We also reconsider the relation between the dataset size, the cluster number, and K in ECBO. Moreover, we verify the effectiveness of the variants of ECBO based on experimental results using synthetic datasets and a benchmark dataset.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.