Constructing three-dimensional discrete Voronoi diagrams by the incremental method and application to self-organizing maps
Takayasu Fuchida, Masayuki Kashima, Hirofumi Nakamura, Kunihiko Mori, Sadayuki Murashima · Systems and Computers in Japan · 2005
We propose an algorithm to construct a three-dimensional (3D) discrete Voronoi diagram using the incremental method on a digitized space and apply it to measure the topology preservation rate of self-organizing maps. The 3D discrete Voronoi diagram needs many pixels and requires much memory and much time to calculate. In this sense, the fast 3D version of the incremental method on a digitized space is useful. Recently, studies of self-organizing feature maps have made it clear that a close relationship exists between feature extraction and the obtaining of masked Delaunay triangulation of input data. Thus, the Voronoi division is becoming an indispensable technique for the study of self organizing feature maps. © 2005 Wiley Periodicals, Inc. Syst Comp Jpn, 36(5): 55–67, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/scj.20205