IEEE Computational Intelligence Magazine - November 2021 - 78

0.02
0.015
0.01
0.005
100
99
98
97
96
95
600 1,2001,8002,4003,0003,6004,2000 600 1,2001,8002,4003,0003,6004,200
Capacity t (bits)
(a)
Capacity t (bits)
(b)
Two Receivers
Three Receivers
Four Receivers
FIGURE 9 Extraction errors and detection accuracies for multiple receivers, (a) extraction error; (b) detection accuracies.
detection accuracies of neural networks
decrease slightly with additional embedded
data. The reason is that there is redundancy
in network parameters. Based on
this, satisfactory detection accuracy can be
guaranteed as long as the value of weight
b in Equation (7) is small enough to
promote the original task of the cover
network. In other words, network parameter
values that simultaneously achieve
data embedding and satisfactory detection
accuracy exist and can be found by training.
Meanwhile, the results in Fig. 8(b)
indicate that the detection accuracy is
stable with increasing capacity. This is
reasonable since the factor dependent on
detection accuracy is the loss weight ,b
which is discussed in the subsection
above. In addition, it can be seen that the
increment of routing iterations does not
make a clear contribution to embedding
capacity and detection accuracy. To save
computational complexity, the number of
routing iterations is determined to be 2 in
the proposed scheme.
For the case of multiple receivers, the
number n of receivers is set as {2, 3, 4},
and the data length t for each receiver is
TABLE III Extraction errors with correct and randomly generated keys.
CAPACITY (BITS)
CORRECT KEYS
RANDOM KEYS I
RANDOM KEYS II
RANDOM KEYS III
RANDOM KEYS IV
RANDOM KEYS V
1000
0.501
0.500
0.503
0.501
0.499
2000
0.501
0.499
0.499
0.500
0.498
3000
0.499
0.502
0.500
0.499
0.501
set as {, ,, }. The results
200 400 3000f
of extraction error e on the MNIST
dataset with batch size 50,
b 15= .,
and 2 routing iterations are shown in
Fig. 9(a). Similarly, the corresponding
values of detection accuracy are shown
in Fig. 9(b). For multiple receivers, the
embedding capacity of each receiver is
less than that of a single receiver. This is
reasonable since the total capacity is
divided into multiple parts. In detail, on
the condition that additional data can be
correctly extracted (),
e 0= the embed4000
0.501
0.501
0.499
0.500
0.500
5000
0.500
0.498
0.499
0.501
0.499
ding
capacity of each receiver is approximately
3000 bits for the case of 2
receivers. For the cases of 3 and 4
receivers, the embedding capacities are
2000 and 1500 bits, respectively, which
is in accordance with the total capacity
of 6000 bits.
As discussed in Subsection III-B, the
TABLE IV Comparisons of embedding capacity.
PROPOSED
SCHEME
EMBEDDING CAPACITY (BITS)
DDA (%)
6000
0.22
METHOD
IN [10]
1024
1.47
METHOD
IN [15]
4096
1.31
additional data cannot be extracted
without the correct keys, since the network
parameters are unknown. To verify
this, a group of experiments are conducted
to test the extraction errors with
correct and randomly generated keys.
The results are listed in Table III, where
five groups of random keys are generated
and marked as " Random keys I " , " Random
keys II " , ..., " Random keys V. " All
the extraction errors are the average
78 IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE | NOVEMBER 2021
Extraction Error e
Detection Accuracy

IEEE Computational Intelligence Magazine - November 2021

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