The nature of statistical learning theory
The nature of statistical learning theory
Hyperparameter selection for self-organizing maps
Neural Computation
Self-organizing maps
GTM: the generative topographic mapping
Neural Computation
Kernel-based equiprobabilistic topographic map formation
Neural Computation
Generative probability density model in the self-organizing map
Self-Organizing neural networks
Faithful Representations and Topographic Maps: From Distortion- to Information-Based Self-Organization
Concrete Mathematics: A Foundation for Computer Science
Concrete Mathematics: A Foundation for Computer Science
Yet another algorithm which can generate topography map
IEEE Transactions on Neural Networks
Self-organizing mixture networks for probability density estimation
IEEE Transactions on Neural Networks
Maximum Likelihood Topographic Map Formation
Neural Computation
Topographic map formation of factorized Edgeworth-expanded kernels
Neural Networks - 2006 Special issue: Advances in self-organizing maps--WSOM'05
Growing kernel-based self-organized maps trained with supervised bias
Intelligent Data Analysis
ICCOMP'05 Proceedings of the 9th WSEAS International Conference on Computers
Information Maximization in a Linear Manifold Topographic Map
Neural Processing Letters
Probabilistic Self-Organizing Graphs
IWANN '09 Proceedings of the 10th International Work-Conference on Artificial Neural Networks: Part I: Bio-Inspired Systems: Computational and Ambient Intelligence
Model-based clustering by probabilistic self-organizing maps
IEEE Transactions on Neural Networks
Probabilistic PCA self-organizing maps
IEEE Transactions on Neural Networks
Multivariate Student-t self-organizing maps
Neural Networks
Self-organization of probabilistic PCA models
IWANN'07 Proceedings of the 9th international work conference on Artificial neural networks
Probabilistic self-organizing maps for continuous data
IEEE Transactions on Neural Networks
Divergence-based vector quantization
Neural Computation
Clustering with kernel-based self-organized maps trained with supervised bias
SIP'06 Proceedings of the 5th WSEAS international conference on Signal processing
Prototype based classification using information theoretic learning
ICONIP'06 Proceedings of the 13th international conference on Neural Information Processing - Volume Part II
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A new learning algorithm for kernel-based topographic map formation is introduced. The kernel parameters are adjusted individually so as to maximize the joint entropy of the kernel outputs. This is done by maximizing the differential entropies of the individual kernel outputs, given that the map's output redundancy, due to the kernel overlap, needs to be minimized. The latter is achieved by minimizing the mutual information between the kernel outputs. As a kernel, the (radial) incomplete gamma distribution is taken since, for a gaussian input density, the differential entropy of the kernel output will be maximal. Since the theoretically optimal joint entropy performance can be derived for the case of nonoverlapping gaussian mixture densities, a new clustering algorithm is suggested that uses this optimum as its "null" distribution. Finally, it is shown that the learning algorithm is similar to one that performs stochastic gradient descent on the Kullback-Leibler divergence for a heteroskedastic gaussian mixture density model.