Topology preservation in self-organizing feature maps: exact definition and measurement

T. Villmann, R. Der, M. Herrmann, T. M. Martinetz

Research output: Contribution to journalArticlepeer-review


The neighborhood preservation of self-organizing feature maps like the Kohonen map is an important property which is exploited in many applications. However, if a dimensional conflict arises this property is lost. Various qualitative and quantitative approaches are known for measuring the degree of topology preservation. They are based on using the locations of the synaptic weight vectors. These approaches, however, may fail in case of nonlinear data manifolds. To overcome this problem, in this paper we present an approach which uses what we call the induced receptive fields for determining the degree of topology preservation. We first introduce a precise definition of topology preservation and then propose a tool for measuring it, the topographic function. The topographic function vanishes if and only if the map is topology preserving. We demonstrate the power of this tool for various examples of data manifolds
Original languageEnglish
Pages (from-to)256-266
Number of pages11
JournalIEEE Transactions on Neural Networks
Issue number2
Publication statusPublished - 1 Mar 1997


  • self-organising feature maps
  • topology
  • Kohonen map
  • dimensional conflict
  • induced receptive fields
  • neighborhood preservation
  • nonlinear data manifolds
  • qualitative approaches
  • quantitative approaches
  • self-organizing feature maps
  • synaptic weight vectors
  • topographic function
  • topology preservation
  • Image processing
  • Informatics
  • Information processing
  • Lattices
  • Network topology
  • Neural networks
  • Research and development
  • Robots
  • Speech processing
  • Vectors


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