Geometrically speaking, the weight vector of codewords of
the adapted units is moved a bit towards the input pixel.
The amount of weight vector movement is guided by a
learning rate, a, decreasing with time. The number of
codewords that are affected by adaptation is determined by
a neighbourhood function, hci which also decreases with
time. This movement makes the distance between these
codewords decrease and, thus, the weight vector of the
codewords becomes more similar to the input pixel. The
respective codeword is more likely to win at future presentations
of this input pixel. The consequence of adapting
not only the winner alone but also a number of codewords
in the neighbourhood of the winner leads to a spatial
clustering of similar input patterns in neighbouring parts of
the K-SOM. Thus, similarities between input pixels that are
presented in the n-dimensional input space are mirrored
within the two-dimensional output space of the K-SOM.
The codebook generation stage of the K-SOM describes a topology preserving mapping from a high-dimensional
input space into a two-dimensional output space where
patterns that are similar in terms of their input space are
mapped to geographically close locations in the output
space.