基于SVD确定NMF初始化矩阵维数

The Dimension of NMF Initialization Matrix Based on SVD

根据奇异值分解和奇异值的属性,提出了确定非负矩阵分解中初始矩阵维数的方法:以矩阵奇异值的平方计算各自的贡献率,以贡献率之和接近给定阈值来确定所需奇异值的个数,并以之为初始矩阵的维数。避免了人为尝试维数的缺陷。给出了相应的证明并解释了方法的合理性。比较了使用奇异值确定初始矩阵维数的不同方法,证明且验证了在相同贡献率的情况下所需初始矩阵维数的大小关系。

Based on the properties of singular value decomposition and singular value, the method of determining the initial matrixdimension of non negative matrix factorization is proposed. The contribution rate of the matrix singular value is calculated. To avoidthe defect of the dimension of human attempt. The rationality of the method is given. A comparison is made on the different methods of determining the initial matrix dimension using the singular values, and it is proved that the size of the initial matrix dimension is required for the same contribution rate.