  We propose a Fourier-based learning algorithm for highly nonlinear multiclass
classification. The algorithm is based on a smoothing technique to calculate
the probability distribution of all classes. To obtain the probability
distribution, the density distribution of each class is smoothed by a low-pass
filter separately. The advantage of the Fourier representation is capturing the
nonlinearities of the data distribution without defining any kernel function.
Furthermore, contrary to the support vector machines, it makes a probabilistic
explanation for the classification possible. Moreover, it can treat overlapped
classes as well. Comparing to the logistic regression, it does not require
feature engineering. In general, its computational performance is also very
well for large data sets and in contrast to other algorithms, the typical
overfitting problem does not happen at all. The capability of the algorithm is
demonstrated for multiclass classification with overlapped classes and very
high nonlinearity of the class distributions.
