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I just have a question on the chosen dimension of Self-organizing map. Typically, an SOM has a dimension of 2 or 3 but rarely larger than that. Is there a particular reason why this is the case?

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SOM can be used for dimension reduction to other dimensions than 2 or 3, but its most common use is for information visualisation, which is most commonly on a 2D screen. For dimensional reduction, SVD (PCA) may be preferable.

Also, although it's a bit of a tangent, a SOM learns the local neighbourhoods. Thus, although the map can be displayed in two dimensions as a sheet, it does not necessarily approach a flat sheet in the original space. Some have justified the use of higher dimension SOMs if higher dimensionality reduces the amount of folding/twisting/wrinkling.

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