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K
C
−
1
(
(
))
(
)
=
det
C
if det
C
0
Diag
C
11
,
C
PP
Otherwise
M
=
(2.15)
1
C
22
,...,
1
where
C
denotes the weight covariance matrix, given by:
i
=
1
v
i
x
ir
x
qr
x
is
x
qs
N
−
−
C
rs
=
∑
,
r
,
s
=
1
,...,
P
(2.16)
N
i
=
1
v
i
∑
BasedonEq.(
2.15
), the weight matrix is switched between a full matrix and a
diagonal matrix. This overcomes possible singularities when the number of training
samples,
N
, is smaller than the dimensionality of the feature space,
P
.
Table
2.2
gives a summary of the OPT-RF method, where the relevance feedback
process is conducted after the initial search.
Table 2.2
Summary of the optimal learning relevance feedback algorithm
=
x
q
Set of vectors to be searched in the database
Input:
Query vector
=
x
n
,
n
=
1
,...,
T
N
i
The training samples
=
{
x
i
}
=
1
S
k
x
q
Output:
The final retrieval set, containing
k
-relevant samples
=
Repeat:
User provides relevance scores of training samples,
v
1
,
v
2
,...,
v
N
v
t
X
Calculate new query:
x
t
q
=
i
∑
1
v
i
=
Calculate weight parameter:
⊨
⊩
K
C
−
1
(
det
(
C
))
if det
(
C
)
=
0
Diag
C
11
,
C
PP
Otherwise
M
=
1
C
22
,...,
1
x
n
x
q
x
q
t
M
x
n
1
2
Calculate
f
q
(
x
n
)=
−
−
,for
n
=
1
,
2
,...,
T
, and obtain
S
k
x
q
=
x
x
k
)
|
f
q
(
x
)
≤
f
q
(
where
S
k
x
q
is the set of nearest neighbors and
x
k
is the
k
-th nearest neighbor
of
x
q
.
S
k
x
q
N
i
=
1
{
x
i
}
ₐ
Until:
User is satisfied with the retrieval result.
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