Database Reference
In-Depth Information
The Mahalonobis inner product leads to the following Mahalonobis distance
between
x
and
x
q
, which is associated as the mapping function as in [
17
,
19
-
24
,
103
],
)=
x
x
q
M
≡
t
M
f
q
(
x
−
(
x
−
x
q
)
(
x
−
x
q
)
(2.11)
P
i
=
1
w
i
(
x
i
−
x
qi
)
2
2
=
(2.12)
P
i
=
1
h
(
d
i
)
2
≡
(2.13)
where
x
q
=
x
q
1
,...,
x
qP
t
is the feature vector of the query image, and
h
(
d
i
)
denotes a transfer function of distance
d
i
=
|
x
i
−
x
qi
|
. The weight parameters
{
w
i
,
i
=
1
1. The weight parameters can be
calculated by the standard deviation criterion [
17
,
20
,
21
] or a probabilistic feature
relevance method [
16
].
Different types of distance function have also been exploited. These include the
selection of Minkowski distance metrics according to a minimum distance within
the positive class [
23
], the selection of metrics based on reinforcement learning [
22
]
and on the interdependencies between feature elements [
25
].
,···,
P
}
are called relevance weights, and
∑
i
w
i
=
2.2.4
Query and Metric Adaptive Method
In order to reduce time for convergence, the adaptive systems have been designed
to combine the query reformulation model with the adaptive similarity function
[
26
-
30
]. Apart from Eq. (
2.8
), the query modification model can be obtained by a
linear discrimination analysis [
30
], and a probabilistic distribution analysis methods
applied to the training samples [
28
].
The optimum solutions for query model and similarity function can be obtained
by the optimal learning relevance feedback (OPT-RF) method [
26
]. The optimum
solution for a query model, obtained by Lagrange multiplier, is given by the
weighted average of the training samples:
v
t
X
∑
x
t
q
=
(2.14)
N
i
=
1
v
i
where
x
q
=
x
q
1
,...,
x
qP
t
t
,
v
i
is the
degree of relevance for the
i
-th training sample given by the user,
X
is the training
sample matrix, obtained by stacking the
N
training vectors into a matrix, i.e.,
X
denotes the new query,
v
=[
v
1
,
v
2
,...,
v
N
]
t
. The optimum solution for the weight matrix
M
is obtained by:
=[
x
1
...
x
N
]
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