自适应超图正则化低秩矩阵分解  

Low-rank matrix factorization with adaptive hypergraph regularizer

作　　者：李毓静 刘奇龙 LI Yujing;LIU Qilong(School of Mathematics Science,Guizhou Normal University,Guiyang,Guizhou 550025,China)

机构地区：[1]贵州师范大学数学科学学院,贵州贵阳550025

出　　处：《贵州师范大学学报（自然科学版）》2023年第4期48-57,76,共11页Journal of Guizhou Normal University：Natural Sciences

基　　金：国家自然科学基金资助项目(12061025);贵州省教育厅自然科学研究资助项目(黔教合KY字[2021]298)。

摘　　要：超图正则化非负矩阵分解(HNMF)是一类常用的数据降维方法。然而,使用预先构造超图的方法不能较好地反映出样本点间的多元关系。为解决此问题,设计了一类自适应超图的构造方法,结合非负矩阵分解,建立了自适应超图正则化低秩矩阵分解(LMFAHR)模型。利用乘性更新的方法求解该模型,并证明了该模型的目标函数在迭代过程中单调不增。数值实验表明:LMFAHR算法与经典的低秩矩阵分解算法相比,在COIL20数据集上评估指标ACC和NMI分别有0.66%~1.48%,0.19%~1.43%的提升,在Yale数据集上评估指标ACC和NMI分别有0.01%~4.29%,0.3%~8.44%的提升。Hypergraph regularized non-negative matrix factorization(HNMF)is a popular class of data dimensionality reduction methods.However,the use of pre-constructed hypergraphs does not better reflect the multivariate relationships among sample points.To solve this problem,a class of adaptive hypergraph construction methods is developed,and a low-rank matrix factorization with adaptive hypergraph regularizer(LMFAHR)model is established in combination with nonnegative matrix factorization.The multiplicative updating method is used to solve the model,and it is proved that the objective function of the model is monotonically non-increasing in the iterative process.The experiments on image datasets COIL20 and Yale show that:Compared to the other algorithms,LMFAHR algorithm improves ACC and NMI by 0.66%~1.48%and 0.19%~1.43%on COIL20 datasets,respectively,and improves ACC and NMI by 0.01%~4.29%and 0.3%~8.44%on Yale datasets,respectively.

关 键 词：矩阵分解 自适应超图 流形学习 聚类 

分 类 号：O241[理学—计算数学]