| Project/Area Number |
18500212
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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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 | Osaka University |
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Principal Investigator |
ADACHI Kohei Osaka University, Graduate School of Human Sciences, Professor (60299055)
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| Co-Investigator(Kenkyū-buntansha) |
ADACHI Kohei Osaka University, Graduate School of Human Sciences, Professor (60299055)
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| Project Period (FY) |
2006 – 2007
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| Project Status |
Completed (Fiscal Year 2007)
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| Budget Amount *help |
¥2,860,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥360,000)
Fiscal Year 2007: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2006: ¥1,300,000 (Direct Cost: ¥1,300,000)
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| Keywords | Multivariate analysis / Joint Procrustes analysis / Principal component analysis / Three-way data / Singular value decomposition / Quartic equation / Semantic differential data / Procrustes rotation / プロクラステス分析 / 交互最小二乗法 |
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| Research Abstract |
These studies concern the principal component analysis performed separately (PCA-SEP) for each frontal slice. of a three-way array of objects x variables x sources, where the slice describes the values of objects on variables for a source. The model of PCA-SEP is found less restrictive than the models of 3-way component analysis (3WCA), but the former has crucial indeterminacy due to which inter-source comparisons of components make no sense. To determine the PCA-SEP solution we propose Joint Procrustes analysis (JPA) in which sources' component score matrices and loading matrices are jointly transformed so that the former matrices match a score matrix common over sources and the latter match a common loading matrix, without any constraint on transformation matrices except their nonsingularity. For minimizing the loss function of JPA which is a function of transformation matrices and their inverse matrices, those are reparameterized by singular value decomposition, which reduces the minimization into solving quartic equations and performing the existing procedures alternately. JPA yields sources' scores and their loadings whose comparisons with each other and across sources make sense, and JPA also gives the common scores and loadings which are used for interpreting components. JPA is illustrated and compared with 3WCA, using an array of semantic differential data. Advantages of JPA include that its solution fits a dataset better and allows us to compare the source differences in scores against those in loadings, but a drawback is that the interpretation of common scores and loadings cannot necessarily be generalized over all sources.
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