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Kohonen's original neighbourhood function was already quite original (minus second derivative of a gaussian, thus strongly attractive at small scale, somewhat repulsive at medium scale and slightly attractive at large scale) ... but i fail to remember convincing theoretical investigations of the neighbourhood function

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The difference of two gaussians has been advocated :

Conference Paper The importance of neighbourhood size in self organising systems

Asymetric neighbourhoods have also been introduced

Article Asymmetric neighborhood functions accelerate ordering proces...

Article Self-Organizing Maps with Asymmetric Neighborhood Function

If you want dynamic neighbourhoods, neural gas will be more appropriate than som but i'd be curious to see a som with an undampded sinusoidal neighbourhood function !

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Kohonen's original neighbourhood function was already quite original (minus second derivative of a gaussian, thus strongly attractive at small scale, somewhat repulsive at medium scale and slightly attractive at large scale) ... but i fail to remember convincing theoretical investigations of the neighbourhood function

.

The difference of two gaussians has been advocated :

Conference Paper The importance of neighbourhood size in self organising systems

Asymetric neighbourhoods have also been introduced

Article Asymmetric neighborhood functions accelerate ordering proces...

Article Self-Organizing Maps with Asymmetric Neighborhood Function

If you want dynamic neighbourhoods, neural gas will be more appropriate than som but i'd be curious to see a som with an undampded sinusoidal neighbourhood function !

.

Part of my research is on a novel type of SOM topological neighborhood function. See ch. 6:

Thesis A SOM Modelling Approach to Behaviour, Cognition and Cogniti...