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points partitioned in the same Voronoi cells have the minimum (overall) encoding
distortion. The movement of the Voronoi vectors is based on the class labels
provided in a training set, so as to improve the accuracy of classification. Let
z
j
J
N
i
=
1
denote the set of training
{
}
j
=
1
denote the set of Voronoi vectors. Also, let
x
i
samples. First, for the input vector
x
i
[
t
]
at iteration index
t
, the class index
c
(
x
i
)
of
the best-matching Voronoi vector
z
c
is identified by:
x
i
−
z
j
c
=
arg min
j
(2.25)
The Voronoi vector
z
c
is modified by the
reinforced learning
rule if the class indexes
of
z
c
and
x
i
are in agreement,
z
c
[
t
+
1
]=
z
c
[
t
]+
ʱ
[
t
](
x
i
[
t
]
−
z
c
[
t
])
(2.26)
Otherwise, the modification is obtained by the
anti-reinforced learning
rule:
z
c
[
t
+
1
]=
z
c
[
t
]
−
ʱ
[
t
](
x
i
[
t
]
−
z
c
[
t
])
(2.27)
where
is the leaning constant, which decreases monotonically with the number
of iterations. All other Voronoi vectors remain unchanged, except the best-matching
Voronoi vector.
In the adaptive image retrieval process, we have the training samples with two-
class labels,
ʱ
[
t
]
N
i
, associated with the query vector,
x
q
. This training
set represents the set of points closest to the query, according to the distance
calculation in the previous search operation. Consequently, each data point can be
regarded as the vector that is
closest
to the Voronoi vector. Therefore, following the
LVQ algorithm, it is observed that all points in this training set are used to modify
only the best-matching Voronoi vector, that is,
z
c
≡
{
x
i
,
l
i
}
,
l
i
∈{
0
,
1
}
=
1
x
q
.
Center shifting model 1:
The first model approximates the Voronoi vector (after the
convergence) by the position that is close to the data points that are in the positive
class (
l
i
=
1), and away from those points that are in the negative class (
l
i
=
0):
+
ʱ
R
x
−
z
ol
c
−
ʱ
N
x
−
z
ol
c
z
new
z
old
=
(2.28)
c
c
N
p
i
1
x
i
N
p
x
=
∑
=
(2.29)
N
n
i
1
x
i
N
n
x
=
∑
=
(2.30)
where
z
old
c
is the previous RBF center,
x
i
,
i
=
1
,...
N
p
are the positive samples,
x
i
,
i
=
1
,...
N
n
are the negative samples,
ʱ
R
and
ʱ
N
are suitable positive constants.
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