非负矩阵分解
乘法函数
单调函数
趋同(经济学)
矩阵分解
分歧(语言学)
算法
梯度下降
数学
基质(化学分析)
不完全Cholesky因式分解
正定矩阵
数学优化
最大化
应用数学
计算机科学
人工智能
特征向量
物理
数学分析
哲学
量子力学
人工神经网络
复合材料
经济
材料科学
经济增长
语言学
作者
Daniel D. Lee,H. Sebastian Seung
摘要
Non-negative matrix factorization (NMF) has previously been shown to be a useful decomposition for multivariate data. Two different multiplicative algorithms for NMF are analyzed. They differ only slightly in the multiplicative factor used in the update rules. One algorithm can be shown to minimize the conventional least squares error while the other minimizes the generalized Kullback-Leibler divergence. The monotonic convergence of both algorithms can be proven using an auxiliary function analogous to that used for proving convergence of the Expectation-Maximization algorithm. The algorithms can also be interpreted as diagonally rescaled gradient descent, where the rescaling factor is optimally chosen to ensure convergence.
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