双流形正则化的主成分分析算法  

Dual-manifold Regularized Principal Component Analysis

作　　者：卢桂馥[1,2] 

机构地区：[1]东南大学信息科学与工程学院,南京210096 [2]安徽工程大学计算机与信息学院,安徽芜湖241000

出　　处：《小型微型计算机系统》2016年第12期2745-2748,共4页Journal of Chinese Computer Systems

基　　金：国家自然科学基金项目(61572033;71371012)资助;安徽高校自然科学研究项目(重大项目)(KJ2015ZD08)资助;教育部人文社会科学规划项目(13YJA630098)资助

摘　　要：针对流形正则化的低秩矩阵分解算法(Manifold Regularized Low-rank Matrix Factorization,MRLMF)只考虑了样本间几何结构这一缺点,提出一种双流形正则化的主成分分析算法(Dual-manifold Regularized Principal Component Analysis,DMRPCA).DM RPCA算法不仅利用样本间的局部几何结构信息来构建Laplacian图,也利用特征间的局部几何结构来构建Laplacian图,并将这两个Laplacian图作为正则化项引入到主成分分析(Principal Component Analysis,PCA)算法目标函数中.然后,设计了一种DMRPCA的求解算法.在实际数据库上的实验表明,DMRPCA算法可以提高现有算法聚类的准确率,从而验证了DMRPCA算法是可行的.To overcome the weakness of the manifold regularized low-rank matrix factorization （MRLMF） method, i. e. , it can only consider the structure of samples, we propose a novel algorithm called dual-manifold regularized principal component analysis （ DMR- PCA ）. DMRPCA not only uses the local geometrical information of samples to construct Laplacian graph, but uses the local geomet- rical information of features to construct Laplacian graph. Then the two Laplacian graph terms are integrated into the objective function of principal component analysis （ PCA ） as the regularization terms. A procedure for solving DMRPCA is also presented in the paper. Experiment results on some real data sets demonstrate that DMRPCA can improve the clustering accuracies of the state-of-the-art algo- rithms, which verified that DMRPCA is efficacious and feasible.

关 键 词：主成分分析 流形正则化 Laplacian图 奇异值分解 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]