L1-norm based fuzzy clustering
Fuzzy Sets and Systems
Fuzzy sets and fuzzy logic: theory and applications
Fuzzy sets and fuzzy logic: theory and applications
Two soft relatives of learning vector quantization
Neural Networks
Reformulating learning vector quantization and radial basis neural networks
Fundamenta Informaticae - Special issue on soft computing
Pattern Recognition with Fuzzy Objective Function Algorithms
Pattern Recognition with Fuzzy Objective Function Algorithms
Generalized fuzzy c-means algorithms
Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
An integrated approach to fuzzy learning vector quantization and fuzzy c-means clustering
IEEE Transactions on Fuzzy Systems
A note on the Gustafson-Kessel and adaptive fuzzy clustering algorithms
IEEE Transactions on Fuzzy Systems
Generalized fuzzy c-means clustering strategies using Lp norm distances
IEEE Transactions on Fuzzy Systems
Optimization of clustering criteria by reformulation
IEEE Transactions on Fuzzy Systems
Repairs to GLVQ: a new family of competitive learning schemes
IEEE Transactions on Neural Networks
An axiomatic approach to soft learning vector quantization and clustering
IEEE Transactions on Neural Networks
IEEE Transactions on Neural Networks
IEEE Transactions on Neural Networks
Integrated Computer-Aided Engineering
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This paper introduces non-Euclidean c-means clustering algorithms. These algorithms rely on weighted norms to measure the distance between the feature vectors and the prototypes that represent the clusters. The proposed algorithms are developed by solving a constrained minimization problem in an iterative fashion. The norm weights are determined from the data in an attempt to produce partitions of the feature vectors that are consistent with the structure of the feature space. A series of experiments on three different data sets reveal that the proposed non-Euclidean c-means algorithms provide an attractive alternative to Euclidean c-means clustering in applications that involve data sets containing clusters of different shapes and sizes.