Abstract: Twin support vector machine is a novel nonparallel binary classification, and its processing speed is much faster than the traditional support vector machine, But the twin support vector machine need to compute the large complex inverse matrices before training. In the nonlinear case, the kernel trick can not be applied directly to the dual optimization problems as traditional SVM, and the twin support vector machine do not consider the effects that different input samples have different effects on the optimal separating hyperplanes. In view of this, this paper proposes a fuzzy simple twin support vector machine. The fuzzy simple support vector machine by dual formulation and Lagrangian improvements, a large number of inverse matrix calculation is omitted, and kernel trick can be directly applied to the non-linear classification; The hybrid fuzzy membership function is not only affected by the distance between each sample point and center, but also affected by neighborhood density of the sample points. Experiments show that, compared with the support vector machines, standard two twin support vector machine, twin bounded support vector machine and fuzzy twin support vector machine, with the hybrid fuzzy membership function of the fuzzy twin support vector machine classification algorithm not only the classification time is short, simple calculation and high accuracy of classification.

Key words: twin support vector machine, support vector machine, inverse matrices, kernel trick, fuzzy membership, classification

摘要： 双支持向量机是一种新的非平行二分类算法，其处理速度比传统支持向量机快很多，但是双支持向量机在训练之前要进行大量的复杂逆矩阵计算；在非线性情况下，它不能像传统支持向量机那样把核技巧直接运用到对偶优化问题中；并且双支持向量机没有考虑不同输入样本点会对最优分类超平面产生不同的影响。针对这些情况，提出了一种模糊简约双支持向量机。该模糊简约双支持向量机通过对二次规划函数和拉格朗日函数的改进，省略大量的逆矩阵计算，同时核技巧能直接运用到非线性分类情况下；对于混合模糊隶属度函数，不仅每个样本点到类中心的距离影响着该混合模糊隶属度，而且该样本点的邻域密度同样影响着该混合模糊隶属度。实验结果表明，与支持向量机、标准双支持向量机、双边界支持向量机、模糊双支持向量机相比，具有该混合模糊隶属度函数的简约双支持向量机不仅分类时间短，计算简单，而且分类精度高。

关键词: 双支持向量机, 支持向量机, 逆矩阵, 核技巧, 模糊隶属度, 分类