  Electromyogram (EMG) classification is a key technique in EMG-based control
systems. The existing EMG classification methods do not consider the
characteristics of EMG features that the distribution has skewness and
kurtosis, causing drawbacks such as the requirement of hyperparameter tuning.
In this paper, we propose a neural network based on the Johnson $S_\mathrm{U}$
translation system that is capable of representing distributions with skewness
and kurtosis. The Johnson system is a normalizing translation that transforms
non-normal data to a normal distribution, thereby enabling the representation
of a wide range of distributions. In this study, a discriminative model based
on the multivariate Johnson $S_\mathrm{U}$ translation system is transformed
into a linear combination of coefficients and input vectors using
log-linearization. This is then incorporated into a neural network structure,
thereby allowing the calculation of the posterior probability of the input
vectors for each class and the determination of model parameters as weight
coefficients of the network. The uniqueness of convergence of the network
learning is theoretically guaranteed. In the experiments, the suitability of
the proposed network for distributions including skewness and kurtosis is
evaluated using artificially generated data. Its applicability for real
biological data is also evaluated via an EMG classification experiment. The
results show that the proposed network achieves high classification performance
without the need for hyperparameter optimization.
