next up previous contents
Next: Convergence: Up: Mathematical treatment Previous: Mathematical treatment

Voronoi region:

The SOM partitions the input space into convex Voronoi regions, each of which corresponds to one unit of the map. The Voronoi region of a map unit i is the union of all vectors tex2html_wrap_inline3156 to which it is the closest one:


In the Voronoi region the reference vector can be shown to be placed according to the local conditional expectation of the data weighted by the neighborhood kernel:


Juha Vesanto
Tue May 27 12:40:37 EET DST 1997