Silhouettes: a graphical aid to the interpretation and validation of cluster analysis
Journal of Computational and Applied Mathematics
Algorithms for clustering data
Algorithms for clustering data
ACM Computing Surveys (CSUR)
Rough Sets: Theoretical Aspects of Reasoning about Data
Rough Sets: Theoretical Aspects of Reasoning about Data
Pattern Recognition with Fuzzy Objective Function Algorithms
Pattern Recognition with Fuzzy Objective Function Algorithms
Center CLICK: A Clustering Algorithm with Applications to Gene Expression Analysis
Proceedings of the Eighth International Conference on Intelligent Systems for Molecular Biology
Interval Set Clustering of Web Users with Rough K-Means
Journal of Intelligent Information Systems
Applied Intelligence
Numerical methods for fuzzy clustering
Information Sciences: an International Journal
Rapid and brief communication: Rough support vector clustering
Pattern Recognition
Some new indexes of cluster validity
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Rough–Fuzzy Collaborative Clustering
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Rough Set Based Generalized Fuzzy -Means Algorithm and Quantitative Indices
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
The possibilistic C-means algorithm: insights and recommendations
IEEE Transactions on Fuzzy Systems
Comments on “A possibilistic approach to clustering”
IEEE Transactions on Fuzzy Systems
A Possibilistic Fuzzy c-Means Clustering Algorithm
IEEE Transactions on Fuzzy Systems
Soft transition from probabilistic to possibilistic fuzzy clustering
IEEE Transactions on Fuzzy Systems
A possibilistic approach to clustering
IEEE Transactions on Fuzzy Systems
RFCM: A Hybrid Clustering Algorithm Using Rough and Fuzzy Sets
Fundamenta Informaticae
A Rough Set Theoretic Approach to Clustering
Fundamenta Informaticae
Bioinformatics and Functional Genomics
Bioinformatics and Functional Genomics
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Cluster analysis is a technique that divides a given data set into a set of clusters in such a way that two objects from the same cluster are as similar as possible and the objects from different clusters are as dissimilar as possible. In this background, different rough-fuzzy clustering algorithms have been shown to be successful for finding overlapping and vaguely defined clusters. However, the crisp lower approximation of a cluster in existing rough-fuzzy clustering algorithms is usually assumed to be spherical in shape, which restricts to find arbitrary shapes of clusters. In this regard, this paper presents a new rough-fuzzy clustering algorithm, termed as robust rough-fuzzy c-means. Each cluster in the proposed clustering algorithm is represented by a set of three parameters, namely, cluster prototype, a possibilistic fuzzy lower approximation, and a probabilistic fuzzy boundary. The possibilistic lower approximation helps in discovering clusters of various shapes. The cluster prototype depends on the weighting average of the possibilistic lower approximation and probabilistic boundary. The proposed algorithm is robust in the sense that it can find overlapping and vaguely defined clusters with arbitrary shapes in noisy environment. An efficient method is presented, based on Pearson's correlation coefficient, to select initial prototypes of different clusters. A method is also introduced based on cluster validity index to identify optimum values of different parameters of the initialization method and the proposed clustering algorithm. The effectiveness of the proposed algorithm, along with a comparison with other clustering algorithms, is demonstrated on synthetic as well as coding and non-coding RNA expression data sets using some cluster validity indices.