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使用支持向量机对非线性可分数据进行分类的基本思想是将样本集映射到一个高维线性空间使其线性可分。文章则基于Jordan曲线定理,提出了一种通用的基于分类超曲面的分类法,它是通过直接构造分类超曲面,根据样本点关于分类曲面的围绕数的奇偶性进行分类的一种新分类判断算法,不需作升维变换,不需要考虑使用何种核函数,而直接地解决非线性分类问题。对数据分类应用的结果说明:基于分类超曲面的分类法可以有效地解决非线性数据的分类问题,并能够提高分类效率和准确度。
The basic idea of using SVM to classify non-linear separable data is to map the sample set into a high-dimensional linear space to make it linearly separable. Based on the Jordan curve theorem, this paper proposes a general classification method based on classification hypersurfaces, which is a new classification judgment by directly constructing the classification hypersurfaces and classifying them according to the parity of the surrounding numbers of the classification surfaces The algorithm does not need to do dimensionless transformation, so it does not need to consider which kind of kernel function to use, but directly solves the problem of nonlinear classification. The results of applying data classification show that the classification based on classification hypersurface can effectively solve the classification problem of nonlinear data and improve the classification efficiency and accuracy.