计算机科学 ›› 2019, Vol. 46 ›› Issue (11): 193-201.doi: 10.11896/jsjkx.181001840
鲁淑霞1,2, 蔡莲香1, 张罗幻1
LU Shu-xia1,2, CAI Lian-xiang1, ZHANG Luo-huan1
摘要: 采用传统的支持向量机方法对含有噪声的数据进行分类时会产生较大的损失,使得分类超平面严重偏离最优超平面,从而导致分类性能较差。为了解决此问题,文中提出了一种鲁棒的支持向量机(Robust Support Vector Machine,RSVM )方法,该方法给出了一种正弦平方形式的损失函数,根据正弦函数的特点,即使对于噪声数据,其损失函数的值也会被限制在[0,1]区间,从而提高了支持向量机的抗噪性。另外,在求解支持向量机时,传统的随机梯度下降方法在每次迭代中利用单个样本梯度近似代替全梯度,这样必然会产生方差,而随着迭代次数的增加,方差也不断累积,从而严重影响算法的分类性能。为了减小方差的影响,引入零阶减小方差的随机梯度下降(Zeroth Order-Stochastic Variance Reduced Gradient,ZO-SVRG )算法。该算法使用坐标梯度估计方法近似代替梯度,通过在每轮迭代中引入梯度修正项来减小方差的影响;同时,采取加权平均的输出形式进行内外循环的输出,加快了优化问题的收敛速度。实验结果表明,提出的基于零阶减小方差方法的鲁棒支持向量机算法对噪声数据具有更好的鲁棒性,且有效降低了方差的影响;为了进一步提高算法的性能,对实验中主要参数λ,k对算法精度的影响进行了分析。对于线性和非线性两种情况,当其参数对(λ,k)分别满足(λ=1,k=5)和(λ=10,k=3)时,可以达到各自的最高精度。
中图分类号:
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