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Reconstruction of a high-dimensional low-rank matrix
http://hdl.handle.net/2241/00145091
http://hdl.handle.net/2241/00145091be59bf8f-5901-4d4b-b663-5ee7463b8f37
名前 / ファイル | ライセンス | アクション |
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EJS_10-1 (414.8 kB)
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Item type | Journal Article(1) | |||||
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公開日 | 2017-01-26 | |||||
タイトル | ||||||
タイトル | Reconstruction of a high-dimensional low-rank matrix | |||||
言語 | ||||||
言語 | eng | |||||
資源タイプ | ||||||
資源 | http://purl.org/coar/resource_type/c_6501 | |||||
タイプ | journal article | |||||
著者 |
Yata, Kazuyoshi
× Yata, Kazuyoshi× Aoshima, Makoto |
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著者別名 |
矢田, 和善
× 矢田, 和善× 青嶋, 誠 |
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抄録 | ||||||
内容記述タイプ | Abstract | |||||
内容記述 | We consider the problem of recovering a low-rank signal matrix in high-dimensional situations. The main issue is how to estimate the signal matrix in the presence of huge noise. We introduce the power spiked model to describe the structure of singular values of a huge data matrix. We first consider the conventional PCA to recover the signal matrix and show that the estimation of the signal matrix holds consistency properties under severe conditions. The conventional PCA is heavily subjected to the noise. In order to reduce the noise we apply the noise-reduction (NR) methodology and propose a new estimation of the signal matrix. We show that the proposed estimation by the NR method holds the consistency properties under mild conditions and improves the error rate of the conventional PCA effectively. Finally, we demonstrate the reconstruction procedures by using a microarray data set. | |||||
書誌情報 |
Electronic Journal of Statistics 巻 10, 号 1, p. 895-917, 発行日 2016 |
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ISSN | ||||||
収録物識別子タイプ | ISSN | |||||
収録物識別子 | 1935-7524 | |||||
DOI | ||||||
識別子タイプ | DOI | |||||
関連識別子 | 10.1214/16-EJS1128 | |||||
著者版フラグ | ||||||
値 | publisher | |||||
出版者 | ||||||
出版者 | Institute of Mathematical Statistics | |||||
出版者 | ||||||
出版者 | Bernoulli Society |