@techreport{oai:ipsj.ixsq.nii.ac.jp:00211737,
 author = {林, 京寿 and 右田, 剛史 and 高橋, 規一 and Keiju, Hayashi and Tsuyoshi, Migita and Norikazu, Takahashi},
 issue = {3},
 month = {Jun},
 note = {非負値行列因子分解 (NMF : Nonnegative Matrix Factorization) は与えられた非負値行列を二つの非負値行列の積で近似することであり，画像処理，音声信号処理，データマイニング，推薦システムなどの幅広い分野に応用されている．最近，NMF の高速計算法の一つである階層的交互最小二乗法を，ネットワークを形成する複数の計算機で分散的に実行する方法が提案された．これにより，単一計算機では扱えないような大規模行列に対しても NMF を高精度で実行することができる．しかし，この方法で用いられている平均合意アルゴリズムでは，合意に至るまでの変数値の履歴をすべて記憶しておかねばならず，各計算機のメモリ使用量や計算負荷が大きくなってしまう．そこで本報告では，平均合意アルゴリズムを単純なものに置き換えた新たな分散計算法を提案し，その有効性を実験的に検証する．特に，不完全な平均合意が NMF の精度にどのように影響するかを実験的に評価する．, Nonnegative Matrix Factorization (NMF) is the process of approximating a given nonnegative matrix by the product of two nonnegative matrices, and has been applied to a wide range of fields such as image processing, audio signal processing, data mining, and recommendation systems. Recently, a distributed computation method has been proposed for multiple computers in a network to execute the hierarchical alternating least squares algorithm, which is well known as a fast computation method for NMF. This method enables us to perform NMF on large matrices with high accuracy, even in the case where they cannot be handled by a single computer. However, the average consensus algorithm used in this method requires each computer to store the entire history of the values of its variables until the complete average consensus is reached, which increases the memory usage and computational cost. In this paper, we propose a new distributed computation method that replaces the average consensus algorithm with a simple one, and verify its effectiveness experimentally. In particular, we experimentally evaluate how incomplete average consensus affects the accuracy of NMF.},
 title = {NMFのための分散HALS法における平均合意アルゴリズムの単純化},
 year = {2021}
}