Fast Rank-1 NMF for Missing Data with KL Divergence
Fast Rank-1 NMF for Missing Data with KL Divergence
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发表时间：
2021-10
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通讯作者：
Kazu Ghalamkari;M. Sugiyama
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作者：
Kazu Ghalamkari;M. Sugiyama
我们提出了一种基于非梯度的缺失数据非负矩阵分解(NMF)的快速方法，称为A1GM，它最小化了从输入矩阵到重构的秩1矩阵的KL发散。我们的方法是基于我们新发现的最佳秩1非负多重矩阵分解(NMMF)的解析封闭公式，NMMF是一种新的非负多重矩阵分解。如果缺失值的位置满足一定的条件，则NMMF可以准确地求解缺失数据的NMF，而A1GM变换给定的矩阵，从而可以应用NMMF的解析解。我们的经验表明，A1GM方法比具有竞争重建误差的梯度方法更有效。
We propose a fast non-gradient-based method of rank-1 non-negative matrix factorization (NMF) for missing data, called A1GM, that minimizes the KL divergence from an input matrix to the reconstructed rank-1 matrix. Our method is based on our new finding of an analytical closed-formula of the best rank-1 non-negative multiple matrix factorization (NMMF), a variety of NMF. NMMF is known to exactly solve NMF for missing data if positions of missing values satisfy a certain condition, and A1GM transforms a given matrix so that the analytical solution to NMMF can be applied. We empirically show that A1GM is more efficient than a gradient method with competitive reconstruction errors.