College of Science, China Agricultural University, Beijing, 100083, China.
College of electronic information and engineering, China Agricultural University, China.
Neural Netw. 2020 Nov;131:201-214. doi: 10.1016/j.neunet.2020.07.030. Epub 2020 Aug 1.
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，称为孪生最小最大概率机（TWMPM），它结合了最小最大概率机（MPM）和孪生支持向量机（TWSVM）的优点。TWMPM 试图构建两个非平行的超平面，使得每个超平面以最大概率分离一类样本，同时远离另一类样本。此外，所提出的 TWMPM 可以通过最小化误分类概率的上界来控制最坏情况下样本的误分类误差。首先提出了一种用于 TWMPM 的有效算法，该算法通过应用多元切比雪夫不等式将 TWMPM 转换为凹分式规划。然后，通过适当的数学变换，将所提出的 TWMPM 重新表述为一对凸二次规划（QP）。这保证了 TWMPM 具有全局最优解，并可以简单有效地求解。此外，我们还为所提出的 TWMPM 开发了一种迭代算法。通过理论上比较这两种提出的算法，可以很容易地知道凸二次规划算法的计算负担低于 TWMPM 的迭代算法。首先构建了一个线性 TWMPM 版本，然后展示了如何利用 Mercer 核来获得非线性 TWMPM 版本。TWMPM 的 QP 算法的计算复杂度与传统的孪生支持向量机（TWSVM）相同。在三个数据库上进行了实验：UCI 基准数据库、实际应用数据库和人工数据库。实验表明，所提出的 TWMPM 及其 QP 算法具有低计算复杂度和较少的参数，具有可行性和有效性。
