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SOMs can be used as a means of learning principal manifolds.

A principal manifold can only be learned correctly using a SOM if

  • the SOM's dimensionality is the same as that of the principal manifold
  • the noise does not 'smear' the manifold too much, thus making it indistinguishable from a manifold with higher dimensionality.
  • there are enough data points to infer the manifold behind the noise.

SOMs tend to have greater unit densities for points in data space with high data density. They do not follow the density strictly, however.

Manifold-mapping is important in visualization. (Think (world) map projection)