Self-organizing maps
GTM: the generative topographic mapping
Neural Computation
Faithful Representations and Topographic Maps: From Distortion- to Information-Based Self-Organization
Robust blind source separation by beta divergence
Neural Computation
Joint entropy maximization in kernel-based topographic maps
Neural Computation
Mutual Information in Learning Feature Transformations
ICML '00 Proceedings of the Seventeenth International Conference on Machine Learning
Kernel-based topographic map formation achieved with an information-theoretic approach
Neural Networks - New developments in self-organizing maps
Generalized relevance learning vector quantization
Neural Networks - New developments in self-organizing maps
Feature extraction by non parametric mutual information maximization
The Journal of Machine Learning Research
Relative information of type s, Csiszár's f-divergence, and information inequalities
Information Sciences—Informatics and Computer Science: An International Journal
Vector quantization using information theoretic concepts
Natural Computing: an international journal
Fuzzy classification by fuzzy labeled neural gas
Neural Networks - 2006 Special issue: Advances in self-organizing maps--WSOM'05
Clustering with Bregman Divergences
The Journal of Machine Learning Research
Non-negative matrix factorization with α-divergence
Pattern Recognition Letters
Robust parameter estimation with a small bias against heavy contamination
Journal of Multivariate Analysis
Bregman Divergences and the Self Organising Map
IDEAL '08 Proceedings of the 9th International Conference on Intelligent Data Engineering and Automated Learning
Patch clustering for massive data sets
Neurocomputing
Nonlinear Dimensionality Reduction
Nonlinear Dimensionality Reduction
The Exploration Machine --- A Novel Method for Data Visualization
WSOM '09 Proceedings of the 7th International Workshop on Advances in Self-Organizing Maps
ICASSP '09 Proceedings of the 2009 IEEE International Conference on Acoustics, Speech and Signal Processing
Cost-sensitive learning based on Bregman divergences
Machine Learning
Sided and symmetrized Bregman centroids
IEEE Transactions on Information Theory
Representation of functional data in neural networks
Neurocomputing
Nonnegative Matrix and Tensor Factorizations: Applications to Exploratory Multi-way Data Analysis and Blind Source Separation
Divergence based online learning in vector quantization
ICAISC'10 Proceedings of the 10th international conference on Artificial intelligence and soft computing: Part I
On Divergences and Informations in Statistics and Information Theory
IEEE Transactions on Information Theory
Functional Bregman Divergence and Bayesian Estimation of Distributions
IEEE Transactions on Information Theory
Sparse functional relevance learning in generalized learning vector quantization
WSOM'11 Proceedings of the 8th international conference on Advances in self-organizing maps
Relevance learning in unsupervised vector quantization based on divergences
WSOM'11 Proceedings of the 8th international conference on Advances in self-organizing maps
Approximation techniques for clustering dissimilarity data
Neurocomputing
Fuzzy supervised self-organizing map for semi-supervised vector quantization
ICAISC'12 Proceedings of the 11th international conference on Artificial Intelligence and Soft Computing - Volume Part I
Fuzzy neural gas for unsupervised vector quantization
ICAISC'12 Proceedings of the 11th international conference on Artificial Intelligence and Soft Computing - Volume Part I
Border-sensitive learning in kernelized learning vector quantization
IWANN'13 Proceedings of the 12th international conference on Artificial Neural Networks: advances in computational intelligence - Volume Part I
Clustering by fuzzy neural gas and evaluation of fuzzy clusters
Computational Intelligence and Neuroscience
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Supervised and unsupervised vector quantization methods for classification and clustering traditionally use dissimilarities, frequently taken as Euclidean distances. In this article, we investigate the applicability of divergences instead, focusing on online learning. We deduce the mathematical fundamentals for its utilization in gradient-based online vector quantization algorithms. It bears on the generalized derivatives of the divergences known as Frééchet derivatives in functional analysis, which reduces in finite-dimensional problems to partial derivatives in a natural way. We demonstrate the application of this methodology for widely applied supervised and unsupervised online vector quantization schemes, including self-organizing maps, neural gas, and learning vector quantization. Additionally, principles for hyperparameter optimization and relevance learning for parameterized divergences in the case of supervised vector quantization are given to achieve improved classification accuracy.