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Related Experiment Videos

Self-organization as an iterative kernel smoothing process

F Mulier1, V Cherkassky

  • 1Department of Electrical Engineering, University of Minnesota, Minneapolis 55455, USA.

Neural Computation
|November 1, 1995
PubMed
Summary
This summary is machine-generated.

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Kohonen

Area of Science:

  • Computational statistics
  • Machine learning
  • Data visualization

Background:

  • Kohonen's self-organizing map (SOM) is a dimensionality reduction technique.
  • Batch processing mode offers computational advantages for SOM training.

Purpose of the Study:

  • To re-interpret the batch self-organizing map (SOM) algorithm.
  • To establish a connection between SOM and kernel smoothing.
  • To propose a generalized SOM algorithm.

Main Methods:

  • Interpreting the batch SOM algorithm as a statistical kernel smoothing problem.
  • Analyzing the role of the neighborhood function and width in SOM.
  • Generalizing SOM by replacing kernel smoothing with nonparametric regression.

Related Experiment Videos

Main Results:

  • The batch SOM algorithm's update step is equivalent to kernel smoothing.
  • The neighborhood function and width in SOM correspond to the kernel and kernel span.
  • The interpretation strengthens the link between SOM and Principal Curve algorithms.

Conclusions:

  • The batch SOM algorithm can be viewed as a statistical kernel smoothing problem.
  • This perspective offers new insights into dimensionality reduction and neighborhood effects.
  • A generalized SOM algorithm is proposed using nonparametric regression methods.