南京大学学报(自然科学版) ›› 2016, Vol. 52 ›› Issue (4): 714.
卢文凯*,景丽萍*,杨 柳
Lu Wenkai*,Jing Liping*,Yang Liu
摘要: 非负矩阵分解算法(Nonnegative Matrix Factorization Algorithm,NMF)已经广泛地应用于诸多领域,但它容易受到异常点的影响.各种针对这个问题的改进方法中,使用L2,1范数的鲁棒非负矩阵算法(Robust Nonnegative Matrix Factorization Algorithm,RNMF)取得了较好的改进效果,但是该算法不能很好的适应数据集异常点比例的变化.针对这一缺点,提出了截断式鲁棒非负矩阵分解算法(Capped Robust Nonnegative Matrix Factorization Algorithm,CRNMF),将去噪比例ε值引入到目标函数中,降低异常点对整体算法的影响.该算法的主要步骤是:在矩阵分解迭代更新的每一步中,计算输入数据与分解因子重构值之间的误差,将误差大于预先设定参数值ε的数据点对应的误差截断为零,重复以上步骤直到收敛.通过ε截断操作,降低基矩阵F和系数矩阵G受异常点的影响.给出了CRNMF的算法描述,并且在模拟数据集和真实数据集进行了实验,实验表明提出的算法与传统的NMF和RNMF相比,可以在一定程度上提高聚类的准确度,减少了异常点对聚类准确度的影响,提高了算法的鲁棒性.
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