鲁棒双参数化间隔支持向量机

Robust Twin Parametric-Margin Support Vector Machine for Pattern Classification

针对不确定数据的二分类问题,提出了一种鲁棒双参数化间隔支持向量机。考虑样本是服从多元高斯分布,并给出了几种协方差矩阵的构造方式。提出的鲁棒双参数化间隔支持向量机通过处理一对较小规模的凸优化问题,寻找两个非平行的参数化间隔超平面,并针对优化问题设计了相应的随机梯度下降算法。当训练样本的方差趋近于零时,鲁棒双参数化间隔支持向量机可退化为传统的双参数化间隔支持向量机。数值实验结果表明,该方法具有较好的泛化性能。

A robust twin parametric-margin support vector machine(R-TPMSVM)is proposed for the binary classification with uncertain domain.More specifically,considering the examples to be multivariate Gaussian distributions with known means and different covariance matrices,R-TPMSVM aims to find two nonparallel parametric-margin hyperplanes from a pair of smaller size convex optimization problems.These optimization problems are solved by stochastic gradient descent method.The formulation of R-TPMSVM approximates the TPMSVM formulation when the training example is an isotropic Gaussian with variance tends to zero.Experimental results show that the proposed approach has comparable generalization.