支持向量机的迭代加权最小二乘拟合：一种优化-最小化算法
Iteratively-Reweighted Least-Squares Fitting of Support Vector Machines: A Majorization--Minimization Algorithm Approach
摘要：
支持向量机是现代数据分析的重要工具。传统上，支持向量机已经通过二次规划来拟合，使用专用的或现成的算法。我们提出了一种替代方法，支持向量机拟合通过优化-最小化（MM）的范例。通过MM算法构造导出的算法可以在每次迭代时单调减少其目标，并且全局收敛到稳定点。我们证明了迭代加权最小二乘（IRLS）算法的建设，通过MM范式，SVM风险最小化问题，涉及铰链，最小二乘，平方铰链，逻辑损失，1-范数，2-范数，和弹性网惩罚。我们的算法的成功实现，通过一些数值例子。
英文摘要：
Support vector machines (SVMs) are an important tool in modern data analysis. Traditionally, support vector machines have been fitted via quadratic programming, either using purpose-built or off-the-shelf algorithms. We present an alternative approach to SVM fitting via the majorization--minimization (MM) paradigm. Algorithms that are derived via MM algorithm constructions can be shown to monotonically decrease their objectives at each iteration, as well as be globally convergent to stationary points. We demonstrate the construction of iteratively-reweighted least-squares (IRLS) algorithms, via the MM paradigm, for SVM risk minimization problems involving the hinge, least-square, squared-hinge, and logistic losses, and 1-norm, 2-norm, and elastic net penalizations. Successful implementations of our algorithms are presented via some numerical examples.
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