多次元データ再構成のための数理計画とその進展

カテゴリ: 論文誌(論文単位)

グループ名: 【C】電子・情報・システム部門

発行日: 2024/02/01

タイトル(英語): Mathematical Programming for Multidimensional Data Reconstruction and Its Progress

著者名: 佐々木　亮平（東京工科大学コンピュータサイエンス学部）

著者名(英語): Ryohei Sasaki (School of Computer Science, Tokyo University of Technology)

キーワード: 行列補完，行列ランク最小化，多様体学習，次元削減，ニューラルネットワーク matrix completion，matrix rank minimization，manifold learning，dimensionality reduction，neural network

要約(英語): Research on reconstructing original data from data that can only be partially observed due to noise or missing data has been ongoing for many years. Such problems are generally referred to as matrix estimation problems. The problem can be formulated when the data to be estimated can be defined as matrix variables in the problem of reconstructing partially observed data. When the properties of the target matrix are unknown, a common approach is a method called matrix rank minimization, which is known for its high estimation accuracy in various fields such as audio, image, and wireless communication. However, this method assumes that the data belong to a linear subspace, and if this assumption is not satisfied, the estimation accuracy significantly deteriorates. Therefore, in recent years, this assumption has been extended to manifolds, and various methods based on this assumption have been proposed. This paper reviews the progress of these methods and describes the latest techniques in this field.

本誌: 電気学会論文誌C（電子・情報・システム部門誌） Vol.144 No.2 （2024） 特集：ディジタル信号処理の基礎と応用

本誌掲載ページ: 43-46 p

原稿種別: 解説／日本語

電子版へのリンク: https://www.jstage.jst.go.jp/article/ieejeiss/144/2/144_43/_article/-char/ja/