A nonlinear projection method based on Kohonen's topology preserving maps

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Abstract
A nonlinear projection method is presented to visualize high-dimensional data as a 2D image. The proposed method is based on the topology preserving mapping algorithm of Kohonen. The topology preserving mapping algorithm is used to train a 2D network structure. Then the interpoint distances in the feature space between the units in the network are graphically displayed to show the underlying structure of the data. Furthermore, we present and discuss a new method to quantify how well a topology preserving mapping algorithm maps the high-dimensional input data onto the network structure. This is used to compare our projection method with a well-known method of Sammon (1969). Experiments indicate that the performance of the Kohonen projection method is comparable or better than Sammon's method for the purpose of classifying clustered data. Its time-complexity only depends on the resolution of the output image, and not on the size of the dataset. A disadvantage, however, is the large amount of CPU time required.