The idea of this algorithm is to find a natural grouping in a set of
data ([SK92], [DH73]. Every data vector is associated
with a point in a d-dimensional data space. The hope is that the
vectors 
of the same class form a cloud or a cluster in data
space. The algorithm presupposes that the vectors 
belonging
to the same class 
are distributed normally with a mean vector
, and that all input vectors are normalized. To
classify a feature vector 
measure the Euclidian distance
from 
to all other mean vectors
and assign 
to the class of the nearest mean. But
what happens if a pattern 
of class 
is assigned
to a wrong class 
? Then for this wrong classified pattern the
two mean vectors 
and 
are moved or
trained in the following way:
which the wrong classified
pattern belongs to, and which is the nearest neighbor to this pattern,
is moved a little bit towards this pattern.
, to which a pattern of class 
is
assigned wrongly, is moved away from it.
The vectors are moved using the rule:
where 
is the weight
between the output 
of a input unit i and a output unit j.
is the learning parameter. By choosing it less or greater than
zero, the direction of movement of a vector can be influenced.
The DLVQ algorithm works in the following way:
. Initialize the net with these vectors. This means:
Generate a unit for every class and initialize its weights with the
corresponding values.
of a class 
is assigned to a class 
then do the following:
which is nearest to 
in its direction.
, to which 
is falsely assigned to away from it.
associated
with a wrong class 
, a new prototype vector 
. For every
class, choose one of the new mean vectors and add it to the
net. Return to step 2.