Tensor Networks for Latent Variable Analysis: Higher Order Canonical Polyadic Decomposition
نویسندگان
چکیده
منابع مشابه
Analysis and Approximation of the Canonical Polyadic Tensor Decomposition
We study the least-squares (LS) functional of the canonical polyadic (CP) tensor decomposition. Our approach is based on the elimination of one factor matrix which results in a reduced functional. The reduced functional is reformulated into a projection framework and into a Rayleigh quotient. An analysis of this functional leads to several conclusions: new sufficient conditions for the existenc...
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Now, the statement (i) follows from (S.1.3) by setting y = x. (ii) Since the vectors ci1 , . . . , ciK−1 are linearly independent in R , it follows that there exists a vector y such that det [ ci1 . . . ciK−1 y ] 6= 0. Hence, by (S.1.3), the (i1, . . . , iK−1)-th column of B(C) is nonzero. (iii) follows from (S.1.3) and the fact that det [ ci1 . . . ciK−1 y ] = 0 if and only if y ∈ span{ci1 , ....
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ژورنال
عنوان ژورنال: IEEE Transactions on Neural Networks and Learning Systems
سال: 2020
ISSN: 2162-237X,2162-2388
DOI: 10.1109/tnnls.2019.2929063