Title of article :
Simplicity of core arrays in three-way principal component analysis and the typical rank of p×q×2 arrays Original Research Article
Author/Authors :
Jos M. F. ten Berge، نويسنده , , Henk A. L. Kiers، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 1999
Pages :
11
From page :
169
To page :
179
Abstract :
Interpreting the solution of a Principal Component Analysis of a three-way array is greatly simplified when the core array has a large number of zero elements. The possibility of achieving this has recently been explored by rotations to simplicity or to simple targets on the one hand, and by mathematical analysis on the other. In the present paper, it is shown that a p×q×2 array, with p>qgreater-or-equal, slanted2, can almost surely be transformed to have all but 2q elements zero. It is also shown that arrays of that form have three-way rank p at most. This has direct implications for the typical rank of p×q×2 arrays, also when p=q. When pgreater-or-equal, slanted2q, the typical rank is 2q; when q q, but it is p when p=q.
Keywords :
Three-way rank , Typical tensorial rank , Candecomp , PARAFAC , Three-mode principalcomponent analysis , Core arrays , Simple structure
Journal title :
Linear Algebra and its Applications
Serial Year :
1999
Journal title :
Linear Algebra and its Applications
Record number :
822755
Link To Document :
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