{
  "id": "2110.12595",
  "version": "v2",
  "published": "2021-10-25T02:05:35.000Z",
  "updated": "2022-02-18T08:31:42.000Z",
  "title": "Fast Rank-1 NMF for Missing Data with KL Divergence",
  "authors": [
    "Kazu Ghalamkari",
    "Mahito Sugiyama"
  ],
  "comment": "16 pages, 5 figures, accepted to the 25th International Conference on Artificial Intelligence and Statistics (AISTATS 2022)",
  "categories": [
    "stat.ML",
    "cs.LG"
  ],
  "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.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-02-18T08:31:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "I.2.6"
    ],
    "keywords": [
      "missing data",
      "kl divergence",
      "non-negative multiple matrix factorization",
      "missing values satisfy",
      "fast non-gradient-based method"
    ],
    "tags": [
      "conference paper"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}