A non-linear projection method based on Kohonen´s topology preserving maps

A nonlinear projection method is presented to visualize high-dimensional data as a two-dimensional image. The proposed method is based on the topology preserving mapping algorithm of Kohonen (1990). This algorithm is used to train a two-dimensional 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. The authors present and discuss some methods to quantify how well a topology preserving mapping algorithm maps the high-dimensional input data onto the network structure. They compare the projection method with the well-known method of Sammon (1969). Experiments indicate that the performance of the Kohonen projection method is comparable or better than Sammon´s method. Another advantage of the method is that its time complexity only depends on the resolution of the output image, and not on the size of the dataset