一种基于局部线性嵌入的非负矩阵分解

Nonnegative matrix factorization based on locally linear embedding

非负矩阵分解(NMF)将一个非负矩阵分类为两个低维的非负子矩阵,算法自提出后已广泛用于模式识别和数据挖掘等领域。但是NMF忽视了矩阵的几何结构,在图像分类、聚类等应用中无法取得较好的效果。在对一些算法分析的基础上,结合局部线性嵌入及正交的思想,文中提出了一种新的非负矩阵算法。实验证明该算法在分类和聚类两方面均具有较好的性能。

Nonnegative matrix factorization(NMF) decomposes a nonnegative dataset into two low-rank nonnegative factor matrices,and is widely used in pattern recognition and data mining since being proposed.However,NMF does not perform well in image classification and clustering because of ignoring the geometric structure of matrix.On the basis of the analysis of some algorithms,this paper proposes a new nonnegative matrix algorithm combining with local linear embedding and orthogonality.The experiments proof the method has good performance in classification and clustering.