Database Reference
In-Depth Information
Center shifting model 2:
We may reduce the procedural parameters and provide a
direct movement of the RBF center towards the positive class. Equation (
2.28
)is
reduced to:
x
−
ʱ
N
x
−
z
ol
c
z
new
c
=
(2.31)
Since the positive class indicates the user's preferred images, the presentation
of
x
for the new RBF center will give a reasonable representation of the desired
images. In particular, the mean value,
x
=
N
p
i
1
N
p
×
∑
1
x
i
, is a statistical measure
providing a good representation of the
i
-th feature component since this is the value
which minimizes the average distance
=
N
p
i
=
1
N
p
×
∑
x
i
−
x
)
(
.
1
2.3.2
Width Selection
The RBFs are adjusted in accordance with different user preferences and different
types of images. Through the proximity evaluation, differential biases are assigned
to each feature, while features with higher relevance degrees are emphasized, and
those with lower degrees are de-emphasized. To estimate the relevance of individual
features, the training vectors associated with the set of positive images are used to
form an
N
p
×
P
feature matrix
R
,
x
1
...
x
N
p
t
x
m
...
R
=
(2.32)
=
x
mi
,
m
=
1
,...,
N
p
,
i
=
1
,...,
P
(2.33)
where
x
mi
is the
i
-th component of the
m
-th feature vector
x
m
,
P
is the total number
of features, and
N
p
is the number of positive samples. As the previous discussion,
the tuning parameter
˃
i
should reflect the relevance of individual features. It was
demonstrated, in [
16
,
34
], that given a particular numerical value
z
i
for a component
of the query vector, the length of the interval which complexly encloses
z
i
and a
pre-determined number
L
of the set of values
x
mi
in the positive set which falls
into its vicinity, is a good indication of the relevancy of the feature. In other
words, the relevancy of the
i
-th feature is related to the density of
x
mi
around
z
i
,
which is inversely proportional to the length of the interval. A large density usually
indicates high relevancy for a particular feature, while a low density implies that
the corresponding feature is not critical to the similarity characterization. Setting
L
N
p
, the set of turning parameters is thus estimated as follows:
RBF width model 1:
=
t
˃
=[
˃
1
,...,
˃
i
,...
˃
P
]
(2.34)
(
x
mi
−
z
i
)
˃
i
=
ʷ
·
max
m
(2.35)
The factor
ʷ
guarantees a reasonably large output
G
(
x
i
,
z
i
)
for the RBF unit, which
indicates the degree of similarity, e.g.,
ʷ
=
3.
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