A Nonlinear Mapping for Data Structure Analysis
IEEE Transactions on Computers
Interactive visualization and analysis of hierarchical neural projections for data mining
IEEE Transactions on Neural Networks
`Neural-gas' network for vector quantization and its application to time-series prediction
IEEE Transactions on Neural Networks
Online data visualization using the neural gas network
Neural Networks - 2006 Special issue: Advances in self-organizing maps--WSOM'05
Effective Visualization of Information Diffusion Process over Complex Networks
ECML PKDD '08 Proceedings of the European conference on Machine Learning and Knowledge Discovery in Databases - Part II
5th Annual International Conference on Mobile and Ubiquitous Systems: Computing, Networking, and Services
Combination of Vector Quantization and Visualization
MLDM '09 Proceedings of the 6th International Conference on Machine Learning and Data Mining in Pattern Recognition
Design of ensemble neural network using entropy theory
Advances in Engineering Software
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A cross-entropy approach to mapping high-dimensional data into a low-dimensional space embedding is presented. The method allows to project simultaneously the input data and the codebook vectors, obtained with the Neural Gas (NG) quantizer algorithm, into a low-dimensional output space. The aim of this approach is to preserve the relationship defined by the NG neighborhood function for each pair of input and codebook vectors. A cost function based on the cross-entropy between input and output probabilities is minimized by using a Newton-Raphson method. The new approach is compared with Sammon's non-linear mapping (NLM) and the hierarchical approach of combining a vector quantizer such as the self-organizing feature map (SOM) or NG with the NLM recall algorithm. In comparison with these techniques, our method delivers a clear visualization of both data points and codebooks, and it achieves a better mapping quality in terms of the topology preservation measure q"m.