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.

翻译：我们为高度非线性多级分类建议了一个基于Fourier的学习算法。 算法基于一种平滑的技术来计算所有分类的概率分布。 为了获得概率分布, 每一类的密度分布由低通道过滤器分别平滑。 Fourier的优点是捕捉数据分布的非线性而不定义任何内核功能。 此外, 与辅助矢量机相反, 它可以对分类进行概率性解释。 此外, 它也可以处理重叠的分类。 比较后勤回归, 它不需要特征工程。 一般而言, 它的计算性能对于大型数据集来说也很好, 与其他算法相比, 典型的超适配问题根本不发生。 算法的能力表现在与重叠的分类和非常高的类别分布非线性上。