Topology representing networks
Neural Networks
Self-Organizing Maps
Visualizing high-dimensional input data with growing self-organizing maps
IWANN'07 Proceedings of the 9th international work conference on Artificial neural networks
Topology preservation in self-organizing feature maps: exact definition and measurement
IEEE Transactions on Neural Networks
A nonlinear projection method based on Kohonen's topology preserving maps
IEEE Transactions on Neural Networks
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Self-organizing map (SOM) is a neural network model widely used in high dimensional data visualization processes. A trained SOM provides a simplified data model as well as a projection of the multidimensional input data into a bi-dimensional plane that reflects the relationships involving the training patters. Visualization methods based in SOM explore different characteristics related to the data learned by the network. It is necessary to find methods to determine the goodness of a trained network in order to evaluate the quality of the high dimensional data visualizations generated using the SOM simplified model. The degree of topology preservation is the most common concept used to implement this measure. Several qualitative and quantitative methods have been proposed for measuring the degree of SOM topology preservation, in particular using Kohonen model. In this work, two measuring topology preservation methods for Growing Cell Structures (GCS) model are proposed: the topographic function and the topology preserving map.