【摘 要】
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We generalize the matrix Kronecker product to tensors and propose the tensor Kro-necker product singular value decomposition (TKPSVD) that decomposes a real
【机 构】
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TheUniversityofHongKong
【出 处】
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2016年张量和矩阵学术研讨会(International conference on Tensor, Matrix a
论文部分内容阅读
We generalize the matrix Kronecker product to tensors and propose the tensor Kro-necker product singular value decomposition (TKPSVD) that decomposes a real k-way tensor A into a linear combination of tensor Kronecker products with an arbitrary number of d factors. For the first time in the literature, we show how to construct A =ΣRj=1σj A(jd)(×)· · ·(×)A(1)j where each factor A(i)j is also a k-way tensor, thus in-cluding matrices (k=2) as a special case. This problem was previously perceived to be very difficult, but we demonstrate it can be readily solved by reshaping and permuting A into a d-way tensor, followed by a orthogonal polyadic decomposition. Moreover, we introduce the new notion of general symmetric tensors (encompassing symmetric, per-symmetric, centrosymmetric, Toeplitz and Hankel tensors, etc.) and prove that when A is structured then its factors A(1)j , . . . , A(d)j will also inherit this structure.
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