Self-organizing maps and boundary effects: quantifying the benefits of torus wrapping for mapping SOM trajectories

In this study the impact of a planar and toroidal self-organizing map (SOM) configuration are investigated with respect to their impact on SOM trajectories. Such trajectories are an encoding of processes within an n-dimensional input data set and offer an important means of visualizing and analyzing process complexity in large n-dimensional problem domains. However, discontinuity associated with boundaries in the standard, planar SOM results in error that limits their analytical use. Previous studies have recommended the use of a toroidal SOM to reduce these errors, but fall short of a fully quantified analysis of the benefits that result. In this study, the comparative analysis of fifteen pairs of identically initiated and trained SOMs, of planar and toroidal configuration, allows the error in trajectory magnitude to be quantified and visualized; both within the SOM and data space. This offers an important insight into the impact of planar SOM boundaries that goes beyond the general, statistical measures of clustering efficacy associated with previous work. The adoption of a toroidal SOM can be seen to improve the distribution of error in the trajectory sets, with the specific spatial configuration of SOM neurons associated with the largest errors changing from those at the corners of the planar SOM to a more complex and less predictable pattern in the toroidal SOM. However, this improvement is limited to the smallest 60% of errors, with torus and planar SOMs performing similarly for the largest 40%.

[1]  H. Ritter.  Self-Organizing Maps on non-euclidean Spaces , 1999 .

[2]  Pragya Agarwal,et al.  Self-Organising Maps , 2008 .

[3]  Uday R. Kulkarni,et al.  Dynamic grouping of parts in flexible manufacturing systems : a self-organizing neural networks approach , 1995 .

[4]  Tereza Cavazos.  Large-scale circulation anomalies conducive to extreme precipitation events and derivation of daily rainfall in northeastern Mexico and southeastern Texas , 1999 .

[5]  Fatimah Ibrahim,et al.  Reexamination of risk criteria in dengue patients using the self-organizing map , 2010, Medical & Biological Engineering & Computing.

[6]  André Skupin,et al.  Visualizing Demographic Trajectories with Self-Organizing Maps , 2005, GeoInformatica.

[7]  P. Mehtala,et al.  Multivariate Techniques for Identifying Diffractive Interactions at the LHC , 2009, 0909.3039.

[8]  Evaristo Jiménez-Contreras,et al.  A connectionist and multivariate approach to science maps: the SOM, clustering and MDS applied to library and information science research , 2006, J. Inf. Sci..

[9]  Kazuhiko Takahashi,et al.  Remarks on human posture classification using self-organizing map , 2004, 2004 IEEE International Conference on Systems, Man and Cybernetics (IEEE Cat. No.04CH37583).

[10]  Alan H. Strahler,et al.  Change-vector analysis in multitemporal space: a tool to detect and categorize land-cover change pro , 1994 .

[11]  Duane DeSieno,et al.  Adding a conscience to competitive learning , 1988, IEEE 1988 International Conference on Neural Networks.

[12]  Teuvo Kohonen,et al.  Visual Explorations in Finance , 1998 .

[13]  Michael Schmuker,et al.  SOMMER: self-organising maps for education and research , 2006, Journal of molecular modeling.

[14]  Erkki Oja,et al.  Kohonen Maps , 1999, Encyclopedia of Machine Learning.

[15]  Sankar K. Pal,et al.  Self-organizing neural network as a fuzzy classifier , 1994, IEEE Trans. Syst. Man Cybern..

[16]  Teuvo Kohonen,et al.  Self-Organizing Maps , 2010 .

[17]  George K. Knopf,et al.  Representing High-Dimensional Data Sets as Closed Surfaces , 2002, Inf. Vis..

[18]  J. Cassano,et al.  Attribution of Projected Changes in Atmospheric Moisture Transport in the Arctic: A Self-Organizing Map Perspective , 2009 .

[19]  André Skupin,et al.  Visualizing Human Movement in Attribute Space , 2008 .

[20]  T. Kohonen,et al.  Visual Explorations in Finance with Self-Organizing Maps , 1998 .

[21]  Kikuo Fujimura,et al.  Spherical and Torus SOM Approaches to Metabolic Syndrome Evaluation , 2007, ICONIP.

[22]  Uday R. Kulkarni,et al.  Circular/wrap-around self-organizing map networks: an empirical study in clustering and classification , 2001, J. Oper. Res. Soc..

[23]  Zhen-Ping Lo,et al.  On the rate of convergence in topology preserving neural networks , 1991, Biological Cybernetics.

[24]  Y. Nishio,et al.  Network-Structured Particle Swarm Optimizer with Various Topology and Its Behaviors , 2009, WSOM.

[25]  Masahiro Takatsuka,et al.  The Geodesic Self-Organizing Map and Its Error Analysis , 2005, ACSC.

[26]  Giles M. Foody,et al.  Applications of the self-organising feature map neural network in community data analysis , 1999 .

[27]  A. Skupin,et al.  Self-organising maps : applications in geographic information science , 2008 .