A parallel topological feature map in APL

ABSTRACT

One can distinguish two different approaches of neural networks the supervised networks and the self organizing or unsupervised neural networks. The first type of neural nets is supplied with an ideal result regarding the input. During the learning procedure, the neural net adjusts weighting factors of the links between neurons so that the input feature vectors map to the ideal output. Those nets are used for example in robotics, where the ideal result is well known: it is the position the robot should be placed in. For the cases where no ideal result is known, the second type of neural nets, the so called self-learning Topological Feature Map (TFM) is appropriate. This paper will introduce such a neural net based on the idea of Kohonen's TFM. The original algorithm was extremely sequential and therefore not suitable for an APL implementation. The parallelization of the algorithm led to important improvements in speed and convergence to the global optimum.

REFERENCES

• 1: H. Bertsch , Joachim Dengler, Klassifizierung und Segmentierung medizinischer Bilder mit Hilfe der selgbstlernenden topologischen Karte, Mustererkennung 1987, 9. DAGM-Symposium, p.166-170, September 29-October 01, 1987
• 2: Diestelmann, W., and B. Kopp, Faktorenanalyse und Clusteranalyse in APL. APL-Journal 7 No. 2, APL-C}Iub Germany e.V. Heidelberg (December 1988): 13
• 3: Kohonen T., Clustering, taxonomy and topological maps of patterns. Sixth International Conference on Pattern Re~mgnition, Munich, Germany (October 1982): 114-128
• 4: Lo, Z.-P., and B. Bavarian, On the rate of convergence in topology preserving neural networks. Biological Cybernetics 65, Springer (1991): 55-63
• 5: H. Ritter , K. Schulten, Convergence properties of Kohonen's topology conserving maps: fluctuations, stability, and dimension selection, Biological Cybernetics, v.60 n.1, p.59-71, Nov. 1988

INDEX TERMS

Primary Classification:
  D. Software
  D.3 PROGRAMMING LANGUAGES
      D.3.2 Language Classifications

          Nouns: APL

Additional Classification:
  I. Computing Methodologies
  I.2 ARTIFICIAL INTELLIGENCE
      I.2.6 Learning
          Subjects: Connectionism and neural nets
  I.4 IMAGE PROCESSING AND COMPUTER VISION

General Terms:
Algorithms, Languages