Spatial global ordering of two-dimensional Kohonen maps

• Main Author: Lim, Marlene Rose T.
• Format: text
• Language: English
• Published: Animo Repository 1998
• Subjects: Computer-algorithms; Spatial analysis (Statistics); Nearest neighbor analysis (Statistics); Mappings (Mathematics); Simulation methods; Computer Sciences
• Online Access: https://animorepository.dlsu.edu.ph/etd_masteral/2040
• Institution: De La Salle University

This paper studies the spatial global ordering of two-dimensional Kohonen Maps. Based solely on the concept of neighbor units correspond to similar values , and independent of the Kohonen algorithm, three metrics are formulated that would measure the disorderliness of the numbering of a two-dimensional map. Six known orders, namely, row or raster-scan order, row-prime order, Morton order, Peano-Hilbert order, Cantor-diagonal order and spiral order are then evaluated using these three order metrics. Among these six known orders, the Cantor-diagonal and the Morton order turn out to be superior in terms of the orderliness of the numbering they produce, while the spiral order is the most inferior. Various simulations were then made on the original and modified versions of Kohonen's self-organizing map algorithm. The resultant (trained) maps, evaluated using again the three order metrics, register measures of disorder that are consistently lower than all the six known orders. This confirms the claim that, indeed, Kohonen Maps are organized in such a way that map units that are geographically close have associated values that are similar. Finally, in order to be able to describe in non-ambiguous terms, the ordering produced by Kohonen's algorithm, a procedure is designed and implemented that lays out typical numberings of Kohonen Maps. There is no formal proof that this procedure is mathematically equivalent to Kohonen's algorithm, this being extremely difficult to produce given that Kohonen Maps are nondeterministic. Nevertheless, this procedure is a concrete formulation of how Kohonen Maps are laid out, in much the same way that the six known orders have precise procedures for laying out their associated numberings.