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oai:ipsj.ixsq.nii.ac.jp:00209011 2025-01-19T15:04:17Z 581:10433:10434

グラフを用いたNMFの地域分散高速化 Graph-based Regional NMF for Distributed Computing 越塚, 毅 竹内, 孝 松林, 達史 澤田, 宏 Koshizuka, Takeshi Koh, Takeuchi Tatsushi, Matsubayashi Hiroshi, Sawada [一般論文（推薦論文）] 行列分解，並列化，分散処理 集計データに対する教師なしのパターン認識技術として，Non-negative Matrix Factorization（NMF）は広く使われている．特にNon-negative Multiple Matrix Factorization（NMMF）では，複数のデータから共通する項目を共通因子として扱い，効果的に同時分解を行う．本研究では共通因子に加え，地域性などの物理的な関係性を持つ集計データに焦点を当て，因子分解を行うrNMF（regional Non-negative Matrix Factorization）を提案する．rNMFは，物理的に距離の近い地域のデータは同様の特徴空間で表現し，分析結果をより直感的に分かりやすいものとする．なお，地域の位置関係はグラフによって与える．さらに分析対象のデータが大規模な行列であっても，グラフの彩色問題をヒューリスティックに解くことで，分散システム上で高速に処理を行える．本稿では，まずrNMFをNMFの拡張として定式化を行い，パラメータ更新法も示す．地域ごとに集計された実データを用いた実験では，rNMFを用いることで，隣接した地域データを共通した特徴空間で表現できること，従来のNMFに対して汎化性能が悪化しないこと，分散システム上で高速に動作することを示す． Non-negative Matrix Factorization (NMF) is a popular unsupervised pattern recognition technique for the analysis of aggregated data. In particular, Non-negative Multiple Matrix Factorization (NMMF) treats common elements from multiple data as common factors, and execute simultaneous decomposition effectively. In this study, we propose a novel matrix factorization method called regional Non-negative Matrix Factorization (rNMF), which factorises multiple matrics simultaneously, focusing on physical relation between aggregated data such as regional characteristics in addition to common factors. rNMF expresses data of physically close areas in a similar feature space, and extracts intuitively interpretable bases and coefficients from multiple matrics. The information of regional location is given by a graph. Furthermore, by solving the graph coloring problem heuristically, rNMF works at high speed on a distributed system even if the analyzed data are large matrices. In this paper, we formulate rNMF as an extended version of NMF and derive multiplicative update rules for parameter estimation. We performed experiment with real data, which were aggregated by region, in order to verify that rNMF can expresses adjacent regional data in a common feature, rNMF attained similar generalization performance as the original NMF, and rNMF works at high speed on a distributed system. 2021-01-15 jpn journal article https://doi.org/10.20729/00208909 https://ipsj.ixsq.nii.ac.jp/records/209011 10.20729/00208909 1882-7764 AN00116647 情報処理学会論文誌 62 1 387 396 https://ipsj.ixsq.nii.ac.jp/record/209011/files/IPSJ-JNL6201046.pdf application/pdf 2.6 MB 2023-01-15