Approximation and radial-basis-function networks
Neural Computation
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
Kernel-based topographic map formation by local density modeling
Neural Computation
Equivariant adaptive source separation
IEEE Transactions on Signal Processing
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
Vector quantization using information theoretic concepts
Natural Computing: an international journal
On the equivalence between kernel self-organising maps and self-organising mixture density networks
Neural Networks - 2006 Special issue: Advances in self-organizing maps--WSOM'05
Mixture density modeling, Kullback-Leibler divergence, and differential log-likelihood
Signal Processing - Special issue: Information theoretic signal processing
Journal of VLSI Signal Processing Systems
Fuzzy labeled self-organizing map with kernel-based topographic map formation
ICANN'07 Proceedings of the 17th international conference on Artificial neural networks
Divergence based online learning in vector quantization
ICAISC'10 Proceedings of the 10th international conference on Artificial intelligence and soft computing: Part I
Divergence-based vector quantization
Neural Computation
The mathematics of divergence based online learning in vector quantization
ANNPR'10 Proceedings of the 4th IAPR TC3 conference on Artificial Neural Networks in Pattern Recognition
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A new information-theoretic learning algorithm is introduced for kernel-based topographic map formation. The kernels are allowed to overlap and move freely in the input space, and to have differing kernel ranges. We start with Linsker's infomax principle and observe that it cannot be readily extended to our case, exactly due to the presence of kernels. We then consider Bell and Sejnowski's generalization of Linsker's infomax principle, which suggests differential entropy maximization, and add a second component to be optimized, namely, mutual information minimization between the kernel outputs, in order to take into account the kernel overlap, and thus the topographic map's output redundancy. The result is joint entropy maximization of the kernel outputs, which we adopt as our learning criterion. We derive a learning algorithm and verify its performance both for a synthetic example, for which the optimal result can be derived analytically, and for a classic real-world example.