Assessing self organizing maps via contiguity analysis.

Contiguity analysis is a straightforward generalization of linear discriminant analysis in which the partition of elements is replaced by a more general graph structure. Applied to the graph induced by a Self Organizing Map (SOM), contiguity analysis provides a set of linear projectors leading to a planar representation as close as possible to the SOM. As expected, such projectors may only concern local parts of the SOMs. They allow us to visualize the shapes of the clusters (convex hulls of the projections of the elements belonging to a cluster) and the pattern of the elements within each cluster. In some contexts, it is possible to project the bootstrap replicates of the elements, and therefore to produce confidence areas for elements via a standard partial bootstrap procedure.