非负矩阵分解与非负张量分解:算法与应用

The algorithm and application of nonnegative matrix factorization and nonnegative tensor factorization

非负张量分解将一个非负张量表为秩1非负张量之和,而非负矩阵分解是非负张量分解在二维下的特殊情形。首先,介绍非负矩阵分解的乘性迭代算法和交替最小二乘算法,并通过数值实验比较两种算法的优劣;其次,介绍非负张量分解在不同代价函数下的乘性迭代算法;最后,将非负矩阵分解和非负张量分解的乘性迭代算法用于人脸识别的特征提取,通过识别准确率比较它们之间的优劣。

The nonnegative tensor factorization(NTF)is to decompose a nonnegative tensor into the sum of some nonnegative tensors of rank one.The nonnegative matrix factorization(NMF)is a special case of NTF in 2D.In this paper,we first introduced the multiplicative iterative algorithm and the alternating least square algorithm of NMF,and compared the advantages and disadvantages of the two algorithms through numerical experiments.Secondly,the multiplicative iterative algorithm of NTF under different cost functions was introduced.Finally,the multiplicative iterative algorithms of NMF and NTF were applied to feature extraction of face recognition.Their advantages and disadvantages were compared by recognition accuracy.