傅立叶变换机器学习方法III：傅立叶分类
Fourier Transform Approach to Machine Learning III: Fourier Classification
摘要：
我们提出了一种基于傅立叶的学习算法高度非线性多类分类。该算法基于平滑技术来计算所有类别的概率分布。为了获得概率分布，每个类别的密度分布分别由低通滤波器平滑。傅立叶表示的优点是捕获数据分布的非线性，而无需定义任何核函数。此外，与支持向量机相反，它使得分类的概率解释成为可能。此外，它还可以处理重叠类。与逻辑回归相比，它不需要特征工程。一般来说，它的计算性能对于大数据集也非常好，与其他算法相比，典型的过拟合问题根本不会发生。该算法的能力被证明为多类分类重叠类和非常高的非线性类分布。
英文摘要：
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.
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