Fast Rank-1 NMF for Missing Data with KL Divergence

@InProceedings{pmlr-v151-ghalamkari22a,
  title = 	 { Fast Rank-1 NMF for Missing Data with KL Divergence },
  author =       {Ghalamkari, Kazu and Sugiyama, Mahito},
  booktitle = 	 {Proceedings of The 25th International Conference on Artificial Intelligence and Statistics},
  pages = 	 {2927--2940},
  year = 	 {2022},
  editor = 	 {Camps-Valls, Gustau and Ruiz, Francisco J. R. and Valera, Isabel},
  volume = 	 {151},
  series = 	 {Proceedings of Machine Learning Research},
  month = 	 {28--30 Mar},
  publisher =    {PMLR},
  pdf = 	 {https://proceedings.mlr.press/v151/ghalamkari22a/ghalamkari22a.pdf},
  url = 	 {https://proceedings.mlr.press/v151/ghalamkari22a.html},
  abstract = 	 { 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. }
}