Ordering Process of Self-Organizing Maps Improved by Asymmetric Neighborhood Function

  • Authors:

  • Takaaki Aoki;Kaiichiro Ota;Koji Kurata;Toshio Aoyagi

  • Affiliations:

  • CREST, JST, Kyoto, Japan 606-8501;Graduate School of Informatics, Kyoto University, Kyoto, Japan 606-8501;Faculty of Engineering, University of the Ryukyus, Okinawa, Japan 903-0213;CREST, JST, Kyoto, Japan 606-8501 and Graduate School of Informatics, Kyoto University, Kyoto, Japan 606-8501

  • Venue:
  • Neural Information Processing
  • Year:
  • 2007

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Abstract

The Self-Organizing Map (SOM) is an unsupervised learning method based on the neural computation, which has recently found wide applications. However, the learning process sometime takes multi-stable states, within which the map is trapped to a 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 found that the required steps for perfect ordering is numerically shown to be reduced from O(N3) to O(N2).