Studies on Joint Prcc ustesAnalysis of Three-Way Data
三向数据联合分析研究
基本信息
- 批准号:18500212
- 负责人:
- 金额:$ 1.83万
- 依托单位:
- 依托单位国家:日本
- 项目类别:Grant-in-Aid for Scientific Research (C)
- 财政年份:2006
- 资助国家:日本
- 起止时间:2006 至 2007
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
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.
这些研究涉及的主成分分析分别进行(PCA-SEP)为每个额叶切片。对象x变量x源的三路数组,其中切片描述了源的变量上的对象的值。PCA-SEP模型比3向成分分析(3 WCA)模型的限制性更小,但前者具有严重的不确定性,因此成分的源间比较没有意义。为了确定PCA-SEP解决方案,我们提出了联合Procrustes分析(JPA),其中源的组件得分矩阵和加载矩阵进行联合变换,使前者的矩阵匹配一个得分矩阵共同的源和后者匹配一个共同的加载矩阵,没有任何约束的变换矩阵,除了他们的非奇异性。为了最小化JPA的损失函数,这是一个功能的转换矩阵和它们的逆矩阵,这些重新参数化的奇异值分解,这减少了最小化为求解四次方程和执行现有的程序交替。JPA产生源代码的分数和它们的负载,它们之间的比较和跨源代码的比较是有意义的,JPA还给出了用于解释组件的公共分数和负载。JPA的说明和比较与3 WCA,使用一个数组的语义差异数据。JPA的优点包括它的解决方案更适合数据集,并允许我们比较源的得分差异与负载差异,但缺点是通用得分和负载的解释不一定适用于所有源。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Statistical Analysis
- DOI:10.1002/9780470089941.eta04as00
- 发表时间:2008-01
- 期刊:
- 影响因子:0
- 作者:John Kloke;Johanna Hardin
- 通讯作者:John Kloke;Johanna Hardin
心理学総合辞典(海保博之・楠見 孝 監修)(3.4節 心理データ解析)
心理学综合辞典(海帆博之、久住隆监修)(第3.4节心理数据分析)
- DOI:
- 发表时间:2006
- 期刊:
- 影响因子:0
- 作者:Kohei;Adachi;Kohei Adachi;足立浩平
- 通讯作者:足立浩平
Principle of Thurstonian scaling, and SD method, In
Thurstonian 标度原理和 SD 方法,In
- DOI:
- 发表时间:2006
- 期刊:
- 影响因子:0
- 作者:Kohei;Adachi;Paired;comparison
- 通讯作者:comparison
On the simplest vector preference model: least-squares component analysis with the unit-length constraint on row loading vectors
最简单的向量偏好模型:行加载向量单位长度约束的最小二乘分量分析
- DOI:
- 发表时间:2007
- 期刊:
- 影响因子:0
- 作者:Kohei;Adachi;Kohei Adachi
- 通讯作者:Kohei Adachi
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ADACHI Kohei其他文献
ADACHI Kohei的其他文献
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{{ truncateString('ADACHI Kohei', 18)}}的其他基金
New Developments in Factor Analysis Underlain by Fixed Models
固定模型下因子分析的新进展
- 批准号:
23500347 - 财政年份:2011
- 资助金额:
$ 1.83万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Studies on principal component analysis for three-way data of inputs and outputs
输入输出三向数据的主成分分析研究
- 批准号:
20500256 - 财政年份:2008
- 资助金额:
$ 1.83万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
New developments in penalized optimal scoring
惩罚性最优评分的新进展
- 批准号:
16500180 - 财政年份:2004
- 资助金额:
$ 1.83万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Psychometric Studies on Quantification and Simple Structure Analysis of Multivariate Categorical Data
多元分类数据量化和简单结构分析的心理测量研究
- 批准号:
13610176 - 财政年份:2001
- 资助金额:
$ 1.83万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Studies on Multidimensional Analysis of Longitudinal Categorical Data
纵向分类数据多维分析研究
- 批准号:
11680330 - 财政年份:1999
- 资助金额:
$ 1.83万 - 项目类别:
Grant-in-Aid for Scientific Research (C)