IEEE Computational Intelligence Magazine - November 2021 - 82

noticed that the embedding capacities
of AlexNet and ResNet18 are much
smaller than that of CapsNets. The reason
for the limitation is that the proposed
scheme is customized for CapsNets so the
performance for other network models
will be inferior to that of CapsNets. Specifically,
the decoding networks are connected
with uji;
t
prediction vector uji;
t
for CapsNets. The
is an important element
in achieving the routing-by-agreement
mecha nism, which is a unique
existence in CapsNets. For other kinds of
networks, suitable elements for data hiding
have not been discovered. Therefore,
there is a limitation in the data hiding
schemes for other networks. For further
study, the universality of the proposed
scheme can be improved.
E. Computational Complexity
A group of experiments is also conducted
to check the computational complexity.
The training time is tested on a
server with the configurations described
at the beginning of Section IV. The
values of training time are shown in
Fig. 16, where the networks are the
same as the original versions when
capacity
t 0= .
650
600
550
500
0 200 400 600 800
Capacity t (bits)
It is clear that the training time of
the stego networks is comparable with
that of the original networks. In other
words, the proposed operation of data
embedding will not increase the training
time. This is reasonable since the added
decoding networks do not participate in
the process of training. The parameters
of data decoding networks are determined
by embedding keys instead of
training. Consequently, the computational
complexity of the proposed
scheme (achieving the operation of data
embedding) is negligible. For this reason,
the computational complexity of
the original network is not analyzed
since it is uncorrelated with the proposed
scheme.
The training time of CapsNets is
much longer than that of AlexNet.
Although the training time is long, CapsNets
perform satisfactorily in some
popular image sets and are promising for
some intelligent tasks, such as multiobject
detection. Note that the long training
time is caused by CapsNets itself
instead of the operation of data hiding.
It can be seen in Fig. 16 that the proposed
operation of data embedding
will not increase the training time. By
CapsNets
1,000 1,200 1,400
FIGURE 16 Computational complexity tested on CapsNets and AlexNet.
15
10
5
0 200 400 600 800
Capacity t (bits)
employing CapsNets for data hiding, the
embedding capacity is approximately
6000 bits with only 400 bits of AlexNet,
which can be seen in Subsections IV-B
and IV-D. In the field of data hiding,
embedding capacity is the most important
indicator since the target of data
hiding is communication.
F. Performance on Other Datasets
To further verify the effectiveness of the
proposed scheme, some experiments are
conducted on the smallNORB dataset
[37], which consists of stereo grayscale
images sized
96 96# The smallNORB
.
dataset contains images of 50 toys
belonging to 5 generic categories: fourlegged
animals, human figures, airplanes,
trucks, and cars. The images are resized
to 32 32# for training and testing. The
architecture employed for smallNORB
is the same as that in Fig. 3, with settings
slightly different, as shown in Fig. 17.
Specifically, the Conv1 layer contains
256 convolutional kernels sized 99#
with a stride of 1 and ReLU activation,
which is the same as the settings for
MNIST. PrimaryCaps contains 32 capsules,
and each capsule contains 8 convolutional
kernels sized 88# with a
AlexNet
1,000 1,200 1,400
ReLU Conv1
ReLU
Conv1
9 × 99×9
9 × 99×9
24
8
FIGURE 17 Architecture of CapsNets for smallNORB.
256
DightCaps
Primary Caps
Primary
Caps
8
32
16
5
8
||L2||
5
...
82 IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE | NOVEMBER 2021
Training Time (s)
Training Time (s)
IEEE Computational Intelligence Magazine - November 2021

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