ササキ　リョウヘイ   佐々木　亮平    所属   コンピュータサイエンス学部 コンピュータサイエンス学科    職種   助教
言語種別	英語
発行・発表の年月	2021/02
形態種別	学術論文
査読	査読あり
標題	Local low-rank approach to nonlinear-matrix completion
執筆形態	共著
掲載誌名	EURASIP Journal on Advances in Signal Processing
掲載区分	国外
出版社・発行元	SpringerOpen
担当区分	筆頭著者,責任著者
著者・共著者	R. Sasaki, K. Konishi, T. Takahashi, and T. Furukawa,
概要	This paper deals with a problem of matrix completion in which each column vector of the matrix belongs to a low-dimensional differentiable manifold (LDDM), with the target matrix being high or full rank. To solve this problem, algorithms based on polynomial mapping and matrix-rank minimization (MRM) have been proposed; such methods assume that each column vector of the target matrix is generated as a vector in a low-dimensional linear subspace (LDLS) and mapped to a pth order polynomial and that the rank of a matrix whose column vectors are dth monomial features of target column vectors is deficient. However, a large number of columns and observed values are needed to strictly solve the MRM problem using this method when p is large; therefore, this paper proposes a new method for obtaining the solution by minimizing the rank of the submatrix without transforming the target matrix, so as to obtain high estimation accuracy even when the number of columns is small. This method is based on the assumption that an LDDM can be approximated locally as an LDLS to achieve high completion accuracy without transforming the target matrix. Numerical examples show that the proposedmethod has a higher accuracy than other low-rank approaches.