Ordering process of self-organizing maps improved by asymmetric neighborhood function

The Self-organizing map (SOM) is an unsupervised learning method based on the neural computation, which has found wide applications. However, the learning process sometime takes multi-stable states, within which the map is trapped to an undesirable disordered state including topological defects on the map. These topological defects critically aggravate the performance of the SOM. In order to overcome this problem, we propose to introduce an asymmetric neighborhood function for the SOM algorithm. Compared with the conventional symmetric one, the asymmetric neighborhood function accelerates the ordering process even in the presence of the defect. However, this asymmetry tends to generate a distorted map. This can be suppressed by an improved method of the asymmetric neighborhood function. In the case of one-dimensional SOM, it is found that the required steps for perfect ordering is numerically shown to be reduced from O(N3) to O(N2). We also discuss the ordering process of a twisted state in two-dimensional SOM, which can not be rectified by the ordinary symmetric neighborhood function.

[1]  Teuvo Kohonen,et al.  Self-Organizing Maps, Third Edition , 2001, Springer Series in Information Sciences.

[2]  D. Hubel,et al.  Sequence regularity and geometry of orientation columns in the monkey striate cortex , 1974, The Journal of comparative neurology.

[3]  C. Malsburg Self-organization of orientation sensitive cells in the striate cortex , 2004, Kybernetik.

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

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

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

[7]  D. Hubel,et al.  Receptive fields, binocular interaction and functional architecture in the cat's visual cortex , 1962, The Journal of physiology.

[8]  S. Amari,et al.  Formation of topographic maps and columnar microstructures in nerve fields , 1979, Biological Cybernetics.

[9]  István Csabai,et al.  Dynamics of the Kohonen map , 1990 .

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

[11]  Toshio Aoyagi,et al.  Self-Organizing Maps with Asymmetric Neighborhood Function , 2007, Neural Computation.

[12]  Roman Bek,et al.  Discourse on one way in which a quantum-mechanics language on the classical logical base can be built up , 1978, Kybernetika.

[13]  Thomas Villmann,et al.  Time behavior of topological ordering in self-organizing feature mapping , 1997, Biological Cybernetics.