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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)⇒