LVQ3.

The same adjustments as in LVQ2 (9) occur, but there is also an extra weight update for the case where all $\mbox{\boldmath$m$}_c \:$, $\mbox{\boldmath$m$}_{c'}$ and $\mbox{\boldmath$x$}$ represent the same class:  

$$\mbox{\boldmath$m$}_i(t+1) = \mbox{\boldmath$m$}_i(t) + \eps... ...lpha(t) [\mbox{\boldmath$x$}(t) - \mbox{\boldmath$m$}_i(t)] \;,$$ (9)

where $\epsilon \in ]0,1[$ is a stabilizing constant factor and $i \in \{c,c'\}$.The value of $\epsilon$ should reflect the width of the adjustment window around the border between classes c and c' so that with a narrow window the stabilizing learning steps (10) are small (i.e. $\epsilon$ is small) [Kohonen, 1990b]. In some cases the window constraint is unnecessary and it can be removed and thus $\epsilon = 1$ applied as suggested in [Kohonen, 1995]. For example, if the reference vectors are carefully initialized, most of the few samples that still satisfy the other update conditions of the LVQ2, exist already around the boundary area [Katagiri and Lee, 1993]. In that case the window constraint may be unnecessary and, may even reject some useful modification and slow down the learning.