Constructing theoretical system for high-dimension, low-sample-size data
Project/Area Number |
23740066
|
Research Category |
Grant-in-Aid for Young Scientists (B)
|
Allocation Type | Multi-year Fund |
Research Field |
General mathematics (including Probability theory/Statistical mathematics)
|
Research Institution | University of Tsukuba |
Principal Investigator |
|
Project Period (FY) |
2011 – 2013
|
Project Status |
Completed (Fiscal Year 2013)
|
Budget Amount *help |
¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
|
Keywords | 高次元小標本データ / 高次元漸近理論 / PCA / 判別分析 / クラスター分析 / マイクロアレイデータ / 高次元小標本 / パスウェイ解析 / 逐次解析 |
Research Abstract |
We proposed statistical theories and methodologies for high-dimension, low-sample-size (HDLSS) data. We showed that HDLSS data have two distinct geometric representations. We proposed the noise-reduction methodology that was brought from the geometric representations. We proposed the extended Cross-data-matrix methodology, which offers an unbiased estimator having small asymptotic variance and low computational cost, for parameters appearing in high-dimensional data analysis. We provided two effective discriminant procedures: a distance-based classifier and a geometric classifier, which can ensure high accuracy in misclassification rates and hold misclassification rates less than a threshold.
|
Report
(4 results)
Research Products
(60 results)