A study on principal points of multivariate distributions
| Project/Area Number |
23700341
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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 |
Statistical science
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| Research Institution | Keio University (2012-2014)
Aoyama Gakuin University (2011) |
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Principal Investigator |
MATSUURA Shun 慶應義塾大学, 理工学部, 助教 (70583368)
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| Project Period (FY) |
2011-04-28 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | 主要点 / Principal points / 楕円対称分布 / 球面対称分布 / 多次元混合分布 / 主部分空間定理 / 主成分ベクトル / 主成分分析 / クラスター分析 / 多変量解析 / 離散近似 |
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| Outline of Final Research Achievements |
A set of k-principal points of a distribution is a set of k points that minimizes the mean squared distance between the random variable (vector) and the nearest point. In this research, the properties and estimation of principal points of multivariate distributions were studied. The main results are the following: (1) Conditions previously obtained for a principal subspace theorem, which ensures that principal points are in a linear subspace spanned by the first several principal components, were extended to more general multivariate distributions. (2) Several new estimators of principal points, some of which are proven to be optimal under some loss function, were derived.
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Report
(5 results)
Research Products
(22 results)
