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Effective PCA for high-dimension, low-sample-size data with noise reduction via geometric representations
http://hdl.handle.net/2241/114069
http://hdl.handle.net/2241/11406907b8bb4c-def0-469c-9edd-dfdc3c2d820f
名前 / ファイル | ライセンス | アクション |
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JMA_105-1.pdf (749.6 kB)
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Item type | Journal Article(1) | |||||
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公開日 | 2011-10-11 | |||||
タイトル | ||||||
タイトル | Effective PCA for high-dimension, low-sample-size data with noise reduction via geometric representations | |||||
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 |
青嶋, 誠
× 青嶋, 誠× 矢田, 和善 |
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抄録 | ||||||
内容記述タイプ | Abstract | |||||
内容記述 | In this article, we propose a new estimation methodology to deal with PCA for high-dimension, low-sample-size (HDLSS) data. We first show that HDLSS datasets have different geometric representations depending on whether a ρ-mixing-type dependency appears in variables or not. When the ρ-mixing-type dependency appears in variables, the HDLSS data converge to an n-dimensional surface of unit sphere with increasing dimension. We pay special attention to this phenomenon. We propose a method called the noise-reduction methodology to estimate eigenvalues of a HDLSS dataset. We show that the eigenvalue estimator holds consistency properties along with its limiting distribution in HDLSS context. We consider consistency properties of PC directions. We apply the noise-reduction methodology to estimating PC scores. We also give an application in the discriminant analysis for HDLSS datasets by using the inverse covariance matrix estimator induced by the noise-reduction methodology. | |||||
書誌情報 |
Journal of multivariate analysis 巻 105, 号 1, p. 193-215, 発行日 2012-02 |
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ISSN | ||||||
収録物識別子タイプ | ISSN | |||||
収録物識別子 | 0047-259X | |||||
書誌レコードID | ||||||
収録物識別子タイプ | NCID | |||||
収録物識別子 | AA0025295X | |||||
DOI | ||||||
識別子タイプ | DOI | |||||
関連識別子 | 10.1016/j.jmva.2011.09.002 | |||||
権利 | ||||||
権利情報 | © 2011 Elsevier Inc. NOTICE: this is the author's version of a work that was accepted for publication in Journal of Multivariate Analysis. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Multivariate Analysis, Vol.105 Issue 1, Pages:193-215. doi: 10.1016/j.jmva.2011.09.002 |
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著者版フラグ | ||||||
値 | author | |||||
出版者 | ||||||
出版者 | Elsevier | |||||
URI | ||||||
識別子 | http://hdl.handle.net/2241/114069 | |||||
識別子タイプ | HDL |