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The Neighbourhood Function



  • The neighbourhood function is greatest for units that are close together (especially the same unit) and decreases as the distance between the two units increases.
  • It is important to realize that neighbourhood refers to the physical proximity of the units not how close their weight vectors are.
  • In BrainWave, the Neighbourhood function is controlled by the MapWeights between units in the Map layer.
  • These weights can be automatically set using the SetNeighbourSize Button.
  • The SetNeighbourSize button determines physical proximity by the number of pixels between the units on the screen - so moving the units will affect how much one unit is affected when a nearby unit wins the competition for an input.
  • The neighbourhood function used:

    N(j, k) = 1/(1 + (d(j, k) / (202 * n2))

    d(j, k) = (xj - xk)2 + (yj - yk)2

    where xj is the x screen coordinate of unit j, yj is the y screen coordinate of unit j, 20 is the width in pixels of a unit (rescaling into unit widths) and n is a neighbourhood size parameter that can be altered to change the rate at which the function decreases.

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