支撑向量机的一致光滑牛顿法

A Uniformly Smoothing Newton Method for Support Vector Machine

摘要: 提升光滑支撑向量机分类性能，本文引入了一种新的一致光滑逼近函数来替代正号函数，此函数不仅克服了支撑向量机模型求解过程中出现的不可微性，也在求解收敛速度上优于其他光滑函数。基于此一致光滑逼近函数我们设计了相应的牛顿算法并证明了该光滑函数的收敛性，最后通过数值模拟体现了该函数在光滑支撑向量机模型中的求解精度、效率和推广适应性的优越性能。

Abstract: To improve the classification performance of smooth support vector machines, a new uniformly smooth approximation function is introduced to replace the positive sign function. It doesn’t only overcome the non-differentiability in the process of solving the support vector machine model, but also is superior to other smooth functions in solving convergence rate. Based on the uniform smooth approximation function, we design a corresponding Newton algorithm and es-tablish the convergence of the proposed algorithm. Finally, numerical simulation shows the su-perior performance of the function in accuracy, efficiency and generalization adaptability for solving the smooth support vector machine model.