Algorithms for Non-negative Matrix Factorization
Algorithms for Non-negative Matrix Factorization
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发表时间：
2000
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通讯作者：
Daniel D. Lee;H. Sebastian;Seung y
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文献类型：
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作者：
Daniel D. Lee;H. Sebastian;Seung y
非负矩阵分解（NMF）以前已被证明是一个有用的多变量数据的分解。分析了NMF的两种不同乘法算法。它们仅在更新规则中使用的乘法因子上略有不同。一种算法可以显示为最小化常规最小二乘误差，而另一种最小化广义Kullback-Leibler散度。这两种算法的单调收敛性可以使用类似于用于证明期望最大化算法的收敛性的辅助函数来证明。该算法也可以被解释为对角重标度梯度下降，其中重标度因子被最佳地选择以确保收敛。
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.