A course in fuzzy systems and control
A course in fuzzy systems and control
Nonlinear component analysis as a kernel eigenvalue problem
Neural Computation
Mixtures of probabilistic principal component analyzers
Neural Computation
Faithful representations with topographic maps
Neural Networks
Kernel PCA and de-noising in feature spaces
Proceedings of the 1998 conference on Advances in neural information processing systems II
Self-Organizing Maps
Joint entropy maximization in kernel-based topographic maps
Neural Computation
A kernel view of the dimensionality reduction of manifolds
ICML '04 Proceedings of the twenty-first international conference on Machine learning
Principal components analysis competitive learning
Neural Computation
Neural Networks: A Comprehensive Foundation (3rd Edition)
Neural Networks: A Comprehensive Foundation (3rd Edition)
TASOM: a new time adaptive self-organizing map
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Limitations of nonlinear PCA as performed with generic neural networks
IEEE Transactions on Neural Networks
Handwritten digit recognition by adaptive-subspace self-organizing map (ASSOM)
IEEE Transactions on Neural Networks
The pre-image problem in kernel methods
IEEE Transactions on Neural Networks
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This article addresses the problem of unsupervised learning of multiple linear manifolds in a topology preserving neural map. The model finds simple linear estimations of the regions of the unknown data manifold. Each neuron of the map corresponds to a linear manifold whose basis and mean vectors and on- and off-manifold standard deviations must be learnt. The learning rules are derived based on competition between neurons and maximizing an approximation of the mutual information between the input and the output of each neuron. Neighborhood functions are also considered in the learning rules in order to develop the topology preserving property for the map. Considering two special density models for the input data, the optimal nonlinear input/output mappings of the neurons are found. Experimental results show a good performance for the proposed method on synthesized and practical problems compared with other relevant techniques.