We propose a new distribution-free Bayes optimal classifier, called the twin minimax probability machine (TWMPM), which combines the benefits of both minimax probability machine(MPM) and twin support vector machine (TWSVM). TWMPM tries to construct two nonparallel hyperplanes such that each hyperplane separates one class samples with maximal probability, and is distant from the other class samples simultaneously. Moreover, the proposed TWMPM can control the misclassification error of samples in a worst-case setting by minimizing the upper bound on misclassification probability. An efficient algorithm for TWMPM is first proposed, which transforms TWMPM into concave fractional programming by applying multivariate Chebyshev inequality. Then the proposed TWMPM is reformulated as a pair of convex quadric programming (QP) by proper mathematical transformations. This guarantees TWMPM to have global optimal solution and be solved simply and effectively. In addition, we develop also an iterative algorithm for the proposed TWMPM. By comparing the two proposed algorithms theoretically, it is easy to know that the convex quadric programming algorithm is with lower computation burden than iterative algorithm for the TWMPM. A linear TWMPM version is first built, and then we show how to exploit mercer kernel to obtain nonlinear TWMPM version. The computation complexity for QP algorithm of TWMPM is in the same order as the traditional twin support vector machine (TWSVM). Experiments are carried out on three databases: UCI benchmark database, a practical application database and an artificial database. With low computation complexity and fewer parameters, experiments show the feasibility and effectiveness of the proposed TWMPM and its QP algorithm.

我们提出了一种新的无分布贝叶斯最优分类器，称为孪生极小极大机（TWMPM），它结合了极小极大概率机（MPM）和孪生支持向量机（TWSVM）的优势。TWMPM试图构造两个不平行的超平面，以使每个超平面以最大的概率分隔一个类别的样本，并且同时远离其他类别的样本。此外，提出的TWMPM可以通过最小化错误分类概率的上限来控制最坏情况下样本的错误分类错误。首先提出了一种有效的TWMPM算法，通过应用多元Chebyshev不等式将TWMPM转换为凹分数编程。然后，通过适当的数学变换将拟议的TWMPM重新构造为一对凸二次规划（QP）。这确保TWMPM拥有全局最优解决方案，并且可以简单有效地解决。此外，我们还为提出的TWMPM开发了一种迭代算法。通过理论上比较这两种算法，可以很容易地知道凸二次规划算法比TWMPM的迭代算法具有更低的计算负担。首先构建线性TWMPM版本，然后说明如何利用Mercer内核获得非线性TWMPM版本。TWMPM的QP算法的计算复杂度与传统的双支持向量机（TWSVM）相同。实验在以下三个数据库上进行：UCI基准数据库，实际应用程序数据库和人工数据库。实验表明，该算法具有较低的计算复杂度和较少的参数，具有可行性和有效性。