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In mathematics, matrix completion is the process of adding entries to a matrix which has some unknown or missing values.〔Charles R. Johnson "Matrix Completion Problems: A Survey", in ''Matrix Theory and Applications'' by Charles R. Johnson 1990 ISBN 0821801546 pagez 171–176 ()〕 In general, given no assumptions about the nature of the entries, matrix completion is theoretically impossible, because the missing entries could be anything. However, given a few assumptions about the nature of the matrix, various algorithms allow it to be reconstructed.〔 Some of the most common assumptions made are that the matrix is low-rank, the observed entries are observed uniformly at random and the singular vectors are separated from the canonical vectors. A well known method for reconstructing low-rank matrices based on convex optimization of the nuclear norm was introduced by Emmanuel Candès and Benjamin Recht.〔''Exact Matrix Completion via Convex Optimization'' by Candès, Emmanuel J. and Recht, Benjamin (2009) in Foundations of Computational Mathematics, 9 (6). pp. 717–772. ISSN 1615-3375 ()〕 == See also == * Imputation * Matrix factorization * Matrix regularization * Sudoku 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Matrix completion」の詳細全文を読む スポンサード リンク
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