CQoCO: A measure for comparative quality of coverage and organization for self-organizing maps

In this paper we introduce a comprehensive measure of quality of coverage and organization in self-organizing maps. The new measure, named CQoCO, combines self-organizing criteria as outlined by Polani, by measuring how, and where neurons are mapped in space and how they are organized. The result is an all-inclusive tool to account for the required properties of a well-organized SOM-untangled coverage of inputs only, reflecting the density of the input space and outlining the natural clusters in the data. The proposed measure has been tested on the traditional version of SOM as well as on a growing version, as proposed by the authors-ParaSOM. While the patterns are simple, the tests also cover a comparison between CQoCO and the measures of quantization error and topological error. The conclusion becomes evident with the progress of the experiments-CQoCO provides an across-the-board measurement of the quality of coverage and organization in SOMs.

[1]  T. Kohonen.  Self-organized formation of topographically correct feature maps , 1982 .

[2]  D. Polani.  Measures for the organization of self-organizing maps , 2001 .

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

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

[5]  Kimmo Kiviluoto,et al.  Topology preservation in self-organizing maps , 1996, Proceedings of International Conference on Neural Networks (ICNN'96).

[6]  Thomas Ottmann,et al.  Algorithms for Reporting and Counting Geometric Intersections , 1979, IEEE Transactions on Computers.

[7]  Bernd Fritzke.  Growing Grid — a self-organizing network with constant neighborhood range and adaptation strength , 1995, Neural Processing Letters.

[8]  Lakhmi C. Jain,et al.  Self-Organizing Neural Networks , 2002 .

[9]  David Zipser,et al.  Feature Discovery by Competive Learning , 1986, Cogn. Sci..

[10]  Klaus Schulten,et al.  Self-organizing maps: ordering, convergence properties and energy functions , 1992, Biological Cybernetics.

[11]  Bernd Fritzke.  Growing Cell Structures – a Self-organizing Network in k Dimensions , 1992 .

[12]  Iren Valova,et al.  Growing mechanisms and cluster identification with TurSOM , 2009, 2009 International Joint Conference on Neural Networks.

[13]  Thomas Villmann,et al.  Topology preservation in self-organizing feature maps: exact definition and measurement , 1997, IEEE Trans. Neural Networks.

[14]  Leon Zurawicki,et al.  Exploring the Brain , 2010 .

[15]  Klaus Schulten,et al.  Self-organizing maps: stationary states, metastability and convergence rate , 1992, Biological Cybernetics.

[16]  M. Paradiso,et al.  Neuroscience: Exploring the Brain , 1996 .

[17]  Anupam Shukla,et al.  Artificial Neural Networks II , 2010 .

[18]  Daniel MacLean,et al.  Role of Initialization in Som Networks - Study of Self-Similar Curve Topologies , 2008 .

[19]  Iren Valova,et al.  A parallel growing architecture for self-organizing maps with unsupervised learning , 2005, Neurocomputing.

[20]  Klaus Pawelzik,et al.  Quantifying the neighborhood preservation of self-organizing feature maps , 1992, IEEE Trans. Neural Networks.

[21]  James L. McClelland,et al.  Parallel distributed processing: explorations in the microstructure of cognition, vol. 1: foundations , 1986 .

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