南京大学学报（自然科学版）2016，Vol.52Issue(4)：714-723,10.DOI:10.13232/j.cnki.jnju.2016.04.016
截断式鲁棒非负矩阵分解算法
Capped robust nonnegative matrix factorization algorithm
摘要
Abstract
Nonnegative Matrix Factorization Algorithm(NMF)has been widely applied in various areas,but it is easily influenced by outliers.In order to solve this problem,researchers have proposed Robust Nonnegative Matrix Factorization Algorithm(RNMF),which uses L2,1 norm to make the normal points be approximate as much as possible and reduce the residual of the outliers by using its absolute rather than square.However,RNMF is still sensitive to the proportion of outliers,i.e.,in some datasets,RNMF can handle outliers well,but its performance in other datasets is not satisfactory.Every real dataset has its own structure,that is,it contains a different proportion of outliers.Because of this,RNMF is limited in practical application.In this article,we present a Capped Robust Nonnegative Matrix Factorization Algorithm (CRNMF)by adding a denoising rateεinto the obj ective function of RNMF.To achieve better controlling of the outliers,we use this algorithm to handle the situation which the real dataset outlier ratio is different.The main idea of CRNMF is evaluating the residual for each data point according to the input data and the factors during the iterative procedure,if the residual is larger than the given denoising rateε, we will set the residual as 0,i.e.,the corresponding data point is taken as outlier and not considered in the computing process.By introducingεtruncation,the algorithm reduced the influence of outliers on matrix F and matrix G.This paper gives the description of CRNMF and experiments on real world and synthetic data sets.Experi-mental results show that the proposed algorithm can improve the clustering accuracy,reduce the impact of outliers and then improve the robustness of the algorithm to some extent,compared with the traditional NMF and RNMF.关键词
去噪比例ε值/L2/1范数/鲁棒性/非负矩阵分解算法(NMF)/鲁棒非负矩阵分解算法(RNMF)Key words
denoising rateε/L2/1 norm/robustness/Nonnegative Matrix Factorization(NMF)/Robust Nonnegative Matrix Factorization Algorithm(RNMF)分类
信息技术与安全科学引用本文复制引用
卢文凯,景丽萍,杨柳..截断式鲁棒非负矩阵分解算法[J].南京大学学报（自然科学版）,2016,52(4):714-723,10.基金项目
国家自然科学基金(61370129,61375062),中央高校基本科研业务费(2014JBM029),CCF-Tencent RAGR(20150116),教育部-中国移动科研基金(MCM20513) （61370129,61375062）
