Fast Rank-1 NMF for Missing Data with KL Divergence

• URL: http://arxiv.org/abs/2110.12595v1
• Date: Mon, 25 Oct 2021 02:05:35 GMT
• Title: Fast Rank-1 NMF for Missing Data with KL Divergence
• Authors: Kazu Ghalamkari, Mahito Sugiyama
• Abstract summary: A1GM minimizes the KL divergence from an input matrix to the reconstructed rank-1 matrix. We show that A1GM is more efficient than a gradient method with competitive reconstruction errors.
• Score: 8.020742121274417
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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