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Supplemental LVQ2.1 Learning Rule (learnlv2)
The following learning rule is one that might be applied after first applying LVQ1. It may improve the result of the first learning. This particular version of LVQ2 (referred to as LVQ2.1 in the literature [Koho97]) is embodied in the function learnlv2. Note again that LVQ2.1 is to be used only after LVQ1 has been applied
Learning here is similar to that in learnlv1 except now two vectors of layer 1 that are closest to the input vector may be updated providing that one belongs to the correct class and one belongs to a wrong class and further providing that the input falls into a "window" near the midplane of the two vectors.
,
(where 
and 
are the Euclidean distances of p from 
and 
respectively). We take a value for 
in the range 0.2 to 0.3. If we pick, for instance, 0.25, then 
. This means that if the minimum of the two distance ratios is greater than 0.6, we adjust the two vectors. i.e., if the input is "near" the midplane, adjust the two vectors providing also that the input vector p and 
belong to the same class, and p and 
do not belong in the same class.
.
Thus, given two vector closest to the input, as long as one belongs to the wrong class and the other to the correct class, and as long as the input falls in a midplane window, the two vectors will be adjusted. Such a procedure allows a vector that is just barely classified correctly with LVQ1 to be moved even closer to the input, so the results are more robust.
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