In this paper, we propose a novel binary classification method called the kernel-free quadratic surface minimax probability machine (QSMPM), that makes use of the kernel-free techniques of the quadratic surface support vector machine (QSSVM) and inherits the advantage of the minimax probability machine (MPM) without any parameters. Specifically, it attempts to find a quadratic hypersurface that separates two classes of samples with maximum probability. However, the optimization problem derived directly was too difficult to solve. Therefore, a nonlinear transformation was introduced to change the quadratic function involved into a linear function. Through such processing, our optimization problem finally became a second-order cone programming problem, which was solved efficiently by an alternate iteration method. It should be pointed out that our method is both kernel-free and parameter-free, making it easy to use. In addition, the quadratic hypersurface obtained by our method was allowed to be any general form of quadratic hypersurface. It has better interpretability than the methods with the kernel function. Finally, in order to demonstrate the geometric interpretation of our QSMPM, five artificial datasets were implemented, including showing the ability to obtain a linear separating hyperplane. Furthermore, numerical experiments on benchmark datasets confirmed that the proposed method had better accuracy and less CPU time than corresponding methods.

中文翻译：

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用于二元分类问题的无核二次曲面极小极大概率机

在本文中，我们提出了一种新的二元分类方法，称为无核二次曲面极小极大概率机（QSMPM），它利用二次曲面支持向量机（QSSVM）的无核技术并继承了没有任何参数的极小极大概率机（MPM）。具体来说，它试图找到一个二次超曲面，以最大概率将两类样本分开。然而，直接推导出的优化问题太难解决了。因此，引入非线性变换将涉及的二次函数变为线性函数。通过这样的处理，我们的优化问题最终变成了一个二阶锥规划问题，可以通过一种交替迭代方法有效地解决。需要指出的是，我们的方法既无内核又无参数，易于使用。此外，通过我们的方法获得的二次超曲面可以是二次超曲面的任何一般形式。它比具有核函数的方法具有更好的可解释性。最后，为了证明我们 QSMPM 的几何解释，实施了五个人工数据集，包括显示获得线性分离超平面的能力。此外，在基准数据集上的数值实验证实，所提出的方法比相应的方法具有更好的准确性和更少的 CPU 时间。它比具有核函数的方法具有更好的可解释性。最后，为了证明我们 QSMPM 的几何解释，实施了五个人工数据集，包括显示获得线性分离超平面的能力。此外，在基准数据集上的数值实验证实，所提出的方法比相应的方法具有更好的准确性和更少的 CPU 时间。它比具有核函数的方法具有更好的可解释性。最后，为了证明我们 QSMPM 的几何解释，实施了五个人工数据集，包括显示获得线性分离超平面的能力。此外，在基准数据集上的数值实验证实，所提出的方法比相应的方法具有更好的准确性和更少的 CPU 时间。