摘要
基于图正则非负矩阵分解(NMF)算法充分利用了高维数据通常位于一个低维流形空间的假设从而构造拉普拉斯矩阵,但该算法的缺点是构造出的拉普拉斯矩阵是提前计算得到的,并没有在乘性更新过程中对它进行迭代。为了解决这个问题,结合子空间学习中的自表示方法生成表示系数,并进一步计算相似性矩阵从而得到拉普拉斯矩阵,而且在更新过程中对拉普拉斯矩阵进行迭代。另外,利用训练集的标签信息构造类别指示矩阵,并引入两个不同的正则项分别对该类别指示矩阵进行重构。该算法被称为图学习正则判别非负矩阵分解(GLDNMF),并给出了相应的乘性更新规则和目标函数的收敛性证明。在两个标准数据集上的人脸识别实验结果显示,和现有典型算法相比,所提算法的人脸识别的准确率提升了1%~5%,验证了其有效性。
The Non-negative Matrix Factorization(NMF)algorithm based on graph regularization makes full use of the assumption that high-dimensional data are usually located in a low-dimensional manifold space to construct the Laplacian matrix.The disadvantage of this algorithm is that the constructed Laplacian matrix is calculated in advance and will not be iterated during the multiplicative update process.In order to solve this problem,the self-representation method in subspace learning was combined to generate the representation coefficient,and the similarity matrix was further calculated to obtain the Laplacian matrix,and the Laplacian matrix was iterated during the update process.In addition,the label information of the training set was used to construct the class indicator matrix,and two different regularization items were introduced to reconstruct the category indicator matrix respectively.This algorithm was called Graph Learning Regularized Discriminative Non-negative Matrix Factorization(GLDNMF),and the corresponding multiplicative update rules and the convergence proof of the objective function were given.Face recognition experimental results on two standard datasets show that the accuracy of the proposed algorithm for face recognition is increased by 1%-5%compared to the existing classic algorithms,verifying the effectiveness of the proposed method.
作者
杜汉
龙显忠
李云
DU Han;LONG Xianzhong;LI Yun(School of Computer Science,Nanjing University of Posts and Telecommunications,Nanjing Jiangsu 210023,China;Jiangsu Key Laboratory of Big Data Security and Intelligent Processing(Nanjing University of Posts and Telecommunications),Nanjing Jiangsu 210023,China)
出处
《计算机应用》
CSCD
北大核心
2021年第12期3455-3461,共7页
journal of Computer Applications
基金
国家自然科学基金青年项目(61906098)。
关键词
非负矩阵分解
自表示
图学习
判别信息
人脸识别
Non-negative Matrix Factorization(NMF)
self-representation
graph learning
discriminative information
face recognition