Fast Rank-1 NMF for Missing Data with KL Divergence
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.
Keywords
Cite
@article{arxiv.2110.12595,
title = {Fast Rank-1 NMF for Missing Data with KL Divergence},
author = {Kazu Ghalamkari and Mahito Sugiyama},
journal= {arXiv preprint arXiv:2110.12595},
year = {2022}
}
Comments
16 pages, 5 figures, accepted to the 25th International Conference on Artificial Intelligence and Statistics (AISTATS 2022)