Sammon's mapping [27] is a non-linear mapping that maps a set of input points on a plane trying to preserve the relative distance between the input points approximately. It can be used to visualize a SOM by mapping the values of codebook vectors on a plane. Furthermore, the topological relations can be drawn using lines between neighboring neurons to enhance the net-like look. Sammon's mapping can be applied directly to data sets, but is computationally very intensive. The SOM quantizes the input data to a small number of codebook vectors, so the burden of computation is not so heavy.
Figure 2.9: Sammon's mapping of the codebook vectors of SOM
The Figure 2.9 is an illustration of the Sammon's mapping. The form of the Sammon's mapping can be considered as a hint of the form of the set of codebook vectors and thus the input data.