自适应图正则化的低秩非负矩阵分解算法

Nonnegative low-rank matrix factorization with adaptive graph neighbors

图正则化(nonnegative matrix factorization,NMF)算法(graph regularization nonnegative matrix factorization,GNMF)仍存在一些不足之处:GNMF算法并没有考虑数据的低秩结构;在GNMF算法中,其拉普拉斯图是使用K近邻(K nearest neighbor,KNN)方法预先定义的,而KNN方法无法总是获得最优图解,从而使得GNMF算法的性能不能达到最优。为此,本文提出了一种自适应图正则化的非负矩阵分解算法(nonnegative low-rank matrix factorization with adaptive graph neighbors,NLMFAN)。一方面,通过引入低秩约束,使得NLMFAN可以获得原始数据集的有效低秩结构;另一方面,设计了一种通过自适应求解相似度矩阵的方法来进行图的构建,即图的构造和矩阵分解的结果被融入一个整体的框架中,使得图中节点的相似性是自动从数据中学习得到的。此外,本文还给出了一种求解NLMFAN的有效算法。在多种数据集上的实验验证了本文所提出的算法的有效性。

The exsting graph regularization nonnegative matrix factorization(GNMF)method still has some shortcom-ings:The GNMF algorithm does not consider the low-rank structure of data.In the GNMF algorithm,the Laplacian graph uses the K-nearest neighbor(KNN)method,and the KNN method cannot always obtain the optimal diagram,which makes the performance of the GNMF algorithm not optimal.For this reason,we propose an algorithm called non-negative low-rank matrix factorization with adaptive graph neighbors(NLMFAN).On the one hand,by introducing low-rank constraints,NLMFAN can obtain the effective low-rank structure of the original dataset.On the other hand,a meth-od for adaptively solving the similarity matrix is designed to construct the graph.This implies that the structure of the graph and the results of the matrix decomposition are integrated into an integrated framework so that the similarity of the nodes in the graph is automatically learned from the data.In addition,an effective algorithm for solving NLMFAN is given,and experiments on a variety of datasets verify the effectiveness of the algorithm.