A case of extreme simplicity of the core matrix in three-mode principal components analysis
A case of extreme simplicity of the core matrix in three-mode principal components analysis
复制标题
三模主成分分析中核心矩阵极其简单的一个案例
DOI：
10.1007/bf02294854
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发表时间：
1998
期刊：
影响因子：
--
通讯作者：
H. Kiers
中科院分区：
文献类型：
--
作者：
Takashi Murakami;J. F. Berge;H. Kiers
在三模主成分分析中，P ×Q ×R核心矩阵G可以在解释之前转换为简单结构。众所周知，当P = QR时，G可以变换为单位矩阵，这意味着所有元素都等于先验指定的值。本文证明，当P = QR−1时，G可以变换为几乎所有元素都等于先验指定的值。本文为这种转换提供了一个封闭形式的解决方案。讨论了G的这种简单结构变换的理论意义和实际意义。
In three-mode Principal Components Analysis, the P ×Q ×R core matrix G can be transformed to simple structure before it is interpreted. It is well-known that, when P = QR, G can be transformed to the identity matrix, which implies that all elements become equal to values specified a priori. In the present paper it is shown that, when P = QR − 1, G can be transformed to have nearly all elements equal to values specified a priori. A closed-form solution for this transformation is offered. Theoretical and practical implications of this simple structure transformation of G are discussed.