The architecture of emergent self-organizing maps to reduce projection errors

There are mainly two types of Emergent Self-Organizing Maps (ESOM) grid structures in use: hexgrid (honeycomb like) and quadgrid (trellis like) maps. In addition to that, the shape of the maps may be square or rectangular. This work investigates the effects of these different map layouts. Hexgrids were found to have no convincing advantage over quadgrids. Rectangular maps, however, are distinctively superior to square maps. Most surprisingly, rectangular maps outperform square maps for isotropic data, i.e. data sets with no particular primary direction.

[1]  Helge J. Ritter,et al.  Neural computation and self-organizing maps - an introduction , 1992, Computation and neural systems series.

[2]  Stephane Zrehen,et al.  Analyzing Kohonen Maps with Geometry , 1993 .

[3]  R. Fisher.  THE USE OF MULTIPLE MEASUREMENTS IN TAXONOMIC PROBLEMS , 1936 .

[4]  D. W. Scott.  A Note on Choices of Bivariate Histogram Bin Shape , 1985 .

[5]  R. Der,et al.  A new quantitative measure of topology preservation in Kohonen's feature maps , 1994, Proceedings of 1994 IEEE International Conference on Neural Networks (ICNN'94).

[6]  Johann Gasteiger,et al.  Classification of multicomponent analytical data of olive oils using different neural networks , 1994 .

[7]  Thomas Villmann,et al.  Neural maps and topographic vector quantization , 1999, Neural Networks.

[8]  Georges Voronoi.  Nouvelles applications des paramètres continus à la théorie des formes quadratiques. Deuxième mémoire. Recherches sur les parallélloèdres primitifs. , 1908 .

[9]  H. Ritter,et al.  Convergence properties of Kohonen's topology conserving maps: fluctuations, stability, and dimension selection , 1988, Biological Cybernetics.

[10]  T. Sejnowski,et al.  A unifying measure for neighbourhood preservation in topographic mappings , 1997 .

[11]  Alfred Ultsch,et al.  Data Mining and Knowledge Discovery with Emergent Self-Organizing Feature Maps for Multivariate Time Series , 1999 .

[13]  James C. Bezdek,et al.  An index of topological preservation and its application to self-organizing feature maps , 1993, Proceedings of 1993 International Conference on Neural Networks (IJCNN-93-Nagoya, Japan).

[14]  Jarkko Venna,et al.  Neighborhood Preservation in Nonlinear Projection Methods: An Experimental Study , 2001, ICANN.

[15]  A. Ultsch.  Maps for the Visualization of high-dimensional Data Spaces , 2003 .

[16]  M. V. Velzen,et al.  Self-organizing maps , 2007 .

[17]  Alfred Ultsch.  Density Estimation and Visualization for Data Containing Clusters of Unknown Structure , 2004, GfKl.

[18]  Teuvo Kohonen,et al.  Self-organized formation of topologically correct feature maps , 2004, Biological Cybernetics.

[19]  Richard Durbin,et al.  A dimension reduction framework for understanding cortical maps , 1990, Nature.