2013 Fiscal Year Final Research Report
Constructing theoretical system for high-dimension, low-sample-size data
| Project/Area Number |
23740066
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | University of Tsukuba |
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Principal Investigator |
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| Project Period (FY) |
2011 – 2013
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| 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 |
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| 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.
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