Database Reference
In-Depth Information
a
(
q
)
mesg
r
(
q
)
ₒ
r
(
t
)
=
×
w
qr
(3.34)
r
⊧
⊨
w
qr
if
g
r
∈ V
q
r
=
1
w
qr
=
w
qr
∑
(3.35)
⊩
0
otherwise
When a signal reaches the video template nodes, only the video template nodes
connected to the query template nodes will be activated. These nodes might send
new signals out, directed towards the video nodes, which are again attenuated by
normalized video template weights
w
jr
derived from the weights
w
jr
, as follows:
mesg
r
(
t
)
ₒ
j
(
v
)
=
mesg
r
(
q
)
ₒ
r
(
t
)
×
w
jr
(3.36)
⊧
⊨
w
jr
if
g
r
∈ V
j
r
=
1
w
jr
w
jr
=
∑
(3.37)
⊩
0
otherwise
Once the signals reach a video node, the activation level of this video node
(associated with the video
V
j
) is given by the sum of the signals (the standard cosine
measure),
R
r
=
1
mesg
r
(
t
)
ₒ
j
(
v
)
a
(
v
)
j
=
(3.38)
R
r
=
1
=
w
qr
w
jr
(3.39)
R
r
1
w
qr
w
jr
∑
=
=
r
=
1
w
qr
(3.40)
R
R
r
=
1
w
jr
∑
∑
This finishes the first round of signal propagation. The network output (i.e.,
a
(
v
)
j
N
) is a desired ranking of the videos for retrieval. The process,
however, does not stop here. The network continues the ever-spreading activation
process after the first round of propagation. This time, however, a minimum
activation threshold is defined such that the video nodes below this threshold send
no signals out. Thus, the activation level at the
r
-th video template node is obtained
by summing up the inputs from the activating video nodes as follows:
,
j
=
1
,...,
a
(
t
)
a
(
v
)
j
=
∑
j
w
jr
(3.41)
r
∈
Pos
where
a
(
v
j
denotes the activation levels of the
j
-th video node and
Pos
is the set of
j
's
such that
a
(
v
)
j
is a threshold value. The activation process is allowed
to continue flowing forwards and backwards between the video template nodes and
≥
ʾ
, where
ʾ
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