Self-organization and associative memory: 3rd edition
Self-organization and associative memory: 3rd edition
Universal approximation using radial-basis-function networks
Neural Computation
NIPS-3 Proceedings of the 1990 conference on Advances in neural information processing systems 3
Approximation and radial-basis-function networks
Neural Computation
Interference cancellation using radial basis function networks
Signal Processing
Two soft relatives of learning vector quantization
Neural Networks
Pattern Recognition with Fuzzy Objective Function Algorithms
Pattern Recognition with Fuzzy Objective Function Algorithms
Artificial Neural Networks: Learning Algorithms, Performance Evaluation, and Applications
Artificial Neural Networks: Learning Algorithms, Performance Evaluation, and Applications
Fast learning in networks of locally-tuned processing units
Neural Computation
An integrated approach to fuzzy learning vector quantization and fuzzy c-means clustering
IEEE Transactions on Fuzzy Systems
Optimization of clustering criteria by reformulation
IEEE Transactions on Fuzzy Systems
Pattern classification using neural networks
IEEE Communications Magazine
Convergence properties of a class of learning vector quantization algorithms
IEEE Transactions on Image Processing
Order statistics learning vector quantizer
IEEE Transactions on Image Processing
Repairs to GLVQ: a new family of competitive learning schemes
IEEE Transactions on Neural Networks
Fuzzy algorithms for learning vector quantization
IEEE Transactions on Neural Networks
A methodology for constructing fuzzy algorithms for learning vector quantization
IEEE Transactions on Neural Networks
A neural-network learning theory and a polynomial time RBF algorithm
IEEE Transactions on Neural Networks
IEEE Transactions on Neural Networks
Orthogonal least squares learning algorithm for radial basis function networks
IEEE Transactions on Neural Networks
Generalized clustering networks and Kohonen's self-organizing scheme
IEEE Transactions on Neural Networks
Evolving space-filling curves to distribute radial basis functions over an input space
IEEE Transactions on Neural Networks
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This paper proposes a framework for developing a broad variety of soft clustering and learning vector quantization (LVQ) algorithms based on gradient descent minimization of a reformulation function. According to the proposed axiomatic approach to learning vector quantization, the development of specific algorithms reduces to the selection of a generator function. A linear generator function leads to the fuzzy c-means (FCM) and fuzzy LVQ (FLVQ) algorithms while an exponential generator function leads to entropy constrained fuzzy clustering (ECFC) and entropy constrained LVQ (ECLVQ) algorithms. The reformulation of clustering and LVQ algorithms is also extended to supervised learning models through an axiomatic approach proposed for reformulating radial basis function (RBF) neural networks. This approach results in a broad variety of admissible RBF models, while the form of the radial basis functions is determined by a generator function. This paper shows that gradient descent learning makes reformulated RBF neural networks an attractive alternative to conventional feed-forward neural networks.