Database Reference
In-Depth Information
2.3
Single-Class Radial Basis Function Based
Relevance Feedback
Whist in the later sections in this chapter, the
P
-dimensional RBF function is
explored, in this section, a one-dimensional Gaussian-shaped RBF applied for the
distance function
h
(
d
i
)
in Eq. (
2.13
), i.e.,
P
i
=
1
G
(
x
i
,
z
i
)
f
q
(
x
)=
(2.21)
i
=
1
exp
2
P
−
(
x
i
−
z
i
)
=
(2.22)
i
2
˃
t
is the
tuning parameter in the form of RBF width. Each RBF unit implements a Gaussian
transformation which constructs a local approximation to a nonlinear input-output
mapping. The magnitude of
f
q
(
t
where
z
=[
z
1
,
z
2
,...
z
P
]
is the center of the RBF,
˃
=[
˃
1
,
˃
2
,...,
˃
P
]
represents the similarity between the input vector
x
and the center
z
, where the highest similarity is attained when
x
x
)
z
.
Each RBF function is characterized by two adjustable parameters, the tuning
parameters and the adjustable center:
=
P
i
{
˃
i
,
z
i
}
(2.23)
=
1
This results in a set of
P
basis functions,
P
i
{
G
i
(
˃
i
,
z
i
)
}
(2.24)
=
1
The parameters are estimated and updated via learning algorithms. For a given
query class, some pictorial features exhibit greater importance or
relevance
than
others in the proximity evaluation [
16
,
30
]. Thus, the expanded set of tuning
parameters,
t
controlled the weighting process according to
the relevance of individual features. If the
i
-th feature is highly relevant, the value
of
˃
=[
˃
1
,
˃
2
,...,
˃
P
]
˃
i
should be small to allow greater sensitivity to any change of the distance
d
i
=
|
˃
i
is assigned to the non-relevant features.
Thus, the magnitude of the corresponding function
G
i
is approximately equal to
unity regardless of the distance
d
i
.
x
i
−
z
i
|
. In contrast, a large value of
2.3.1
Center Selection
The selection of query location is done by a modified version of the learning
quantization (LVQ) method [
31
]. In the LVQ process, the initial vectors (in a
codebook), referred to as Voronoi vectors, are modified in such a way that all
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