While the u-matrix is a good method for visualizing clusters, it does not provide a very clear picture of the overall shape of the data space because the visualization is tied to the map grid. To visualize the shape of the SOM in the input space, some projection method can be used, e.g. the Sammon's projection .
The Sammon's projection performs a non-linear projection from the input space to a lower dimension, typically to a plane. The algorithm tries to preserve all distances between input vectors, emphasizing local distances. The method is iterative and computationally heavy. However, when applied to the weight vectors of a SOM as opposed to the whole original data set, the computing times of the algorithm stay reasonable. In visualization the projections of neighboring reference vectors are usually connected by lines, as seen in figure 2.7. The Sammon's projection of a SOM gives a very informative picture of the global shape and the overall smoothness of the SOM. A defect with the Sammon's projection is that it cannot be used to project new points, or points that were not used in the training phase, on the output plane.
Figure 2.7: Sammon's projection of a SOM. The projections of the map units of the SOM are depicted as small black dots. Units are connected to their neighbors with lines.