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Page 6 of 19 Ao et al. Intell Robot 2023;3(4):495-513 I http://dx.doi.org/10.20517/ir.2023.28

∑ ∑ ∑
1
= (3)

To generate the locality map of the modified image classification constructs, as described above, the order of

summation should be exchanged to obtain , and then the score is calculated as
CAM
1 ∑ ∑ ∑

= (4)

Grad-CAM can help us understand the process of predicting gestures in CNN models. The high-importance
feature region obtained by Grad-CAM allows us to intuitively understand which regions have a greater impact
on the network, by which we can invert their corresponding muscles and thus understand which muscles
produce more information for that labeled gesture to enable the network to perform the recognition task. On
the other hand, this high-importance feature region also helps us to narrow down the channel information
interaction and reduces a lot of redundant information for muscle synergy analysis.

2.4. Muscle Synergy Analysis
The total reward value of the gesture recognition process is the output ( ) obtained with all the input in-
formation entered into the network minus the output (∅) obtained without any information entered into
the network. Here, ’∅’ denotes an empty input. The total contribution value obtained from the ten electrode
channel inputs needs to be fairly distributed to each channel, and to fairly calculate the contribution of each
channel individually, we use the Shapley value to consider the effect of the participation or non-participation
of that channel in the input on the results for different gesture recognition situations [23] . Therefore, the Shapley
value for each input information about the channel is measured as

∑
(| | − | | − 1)! | |! [ ( ) ]
∅ Shapley ( ) = ∪{ } − ( ) (5)
| |!
⊆ \{ }
∅ Shapley ( ) is the Shapley value for the input . is the number of electrodes participating in the input, and is
the total number of electrodes. in formulas is the ten electrode channel information, and ( ) denotes the
output of the neural network obtained from the input . Previous studies have focused on the interactions
between two variables. Given an input and a total number of participants , the total reward for all channels
is calculated as

∑
| ( ) − (0)| = (6)
=1
There is a simple definition of interaction. If the input contains channels, and the information of these
channels always functions together as input, then these channels can be considered to form a coalition.
The coalition can receive a reward, denoted by . It is usually different from when a single channel acts alone
∑
to participate in the game. The additional bonus − ∈ received by the alliance can be quantified as an
∑
interaction. If − ∈ > 0, we consider that the participants in the coalition have a positive influence. On
the contrary, it means that there is a negative or antagonistic effect between the group of variables.

However, this equation for measuring interactions can only be used in a single alliance. Their interactions
are either purely positive or purely negative. We first discuss the interaction between two single channels