| Project/Area Number |
22300094
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Statistical science
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| Research Institution | University of Tsukuba |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
YATA Kazuyoshi 筑波大学, 数理物質系, 助教 (90585803)
SATO-ILIC Mika 筑波大学, システム情報系, 教授 (60269214)
AKAHIRA Masafumi 筑波大学, 名誉教授 (70017424)
KOIKE Ken-ichi 筑波大学, 数理物質系, 准教授 (90260471)
OHYAUCHI Nao 筑波大学, 数理物質系, 助教 (40375374)
高橋 秀人 筑波大学, 医学医療系, 准教授 (80261808)
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| Project Period (FY) |
2010-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥17,940,000 (Direct Cost: ¥13,800,000、Indirect Cost: ¥4,140,000)
Fiscal Year 2014: ¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2013: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2012: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2011: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2010: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
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| Keywords | 高次元データ解析 / 多変量解析 / 主成分分析 / 判別分析 / クラスター分析 / ノイズ掃き出し法 / クロスデータ行列法 / マイクロアレイデータ / 高次元データ / パターン認識 / ネットワーク / 幾何学的表現 / 相関検定 / 標本数決定 / グラフィカルモデル / パスウェイ解析 / 多重検定 / 漸近正規性 / 標本数 / 高次元小標本 / HDLSS / 高次元漸近理論 / 変数選択 / 情報量 |
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| Outline of Final Research Achievements |
We created two high-dimensional PCAs which we called the noise-reduction methodology and cross-data-matrix methodology. We proposed a new model, the power spiked model, for eigenvalues and gave consistent estimators of the eigenvalues, eigenvectors and PC scores. We did pioneering work on band-width confidence regions, two-sample problems, classification, variable selection, regression, pathway analysis and so on. We created the extended cross-data-matrix methodology which gives an unbiased estimator at low cost and applied it to the test of correlations. We considered multiclass discriminant analysis and showed that the distance-based classifier, geometric classifier and feature selection by DQDA are superior to sparse regularized classifiers. We proved their misclassification rates go to zero in high-dimension, non-sparse settings. Our work can be applied to many fields, such as medicine and big data, and has much lower computational costs with higher accuracy than existing methods.
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