Carto-SOM: cartogram creation using self-organizing maps
International Journal of Geographical Information Science
Learning Highly Structured Manifolds: Harnessing the Power of SOMs
Similarity-Based Clustering
Cartograms, Self-Organizing Maps, and Magnification Control
WSOM '09 Proceedings of the 7th International Workshop on Advances in Self-Organizing Maps
Exploiting data topology in visualization and clustering of self-organizing maps
IEEE Transactions on Neural Networks
Adaptive FIR neural model for centroid learning in self-organizing maps
IEEE Transactions on Neural Networks
A sequential algorithm for training the SOM prototypes based on higher-order recursive equations
Advances in Artificial Neural Systems
Vector quantization based approximate spectral clustering of large datasets
Pattern Recognition
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In this paper, we examine the scope of validity of the explicit self-organizing map (SOM) magnification control scheme of Bauer (1996) on data for which the theory does not guarantee success, namely data that are n-dimensional, nges2, and whose components in the different dimensions are not statistically independent. The Bauer algorithm is very attractive for the possibility of faithful representation of the probability density function (pdf) of a data manifold, or for discovery of rare events, among other properties. Since theoretically unsupported data of higher dimensionality and higher complexity would benefit most from the power of explicit magnification control, we conduct systematic simulations on "forbidden" data. For the unsupported n=2 cases that we investigate, the simulations show that even though the magnification exponent alphaachieved achieved by magnification control is not the same as the desired alphadesired, alphaachieved systematically follows alphadesired with a slowly increasing positive offset. We show that for simple synthetic higher dimensional data information, theoretically optimum pdf matching (alphaachieved=1) can be achieved, and that negative magnification has the desired effect of improving the detectability of rare classes. In addition, we further study theoretically unsupported cases with real data