【摘 要】
：
The completely positive (CP) tensor verification and decomposition are essential in tensor analysis and computation due to the wide applications in statisti
【机 构】
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BeijingJiaoTongUniversity
【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
The completely positive (CP) tensor verification and decomposition are essential in tensor analysis and computation due to the wide applications in statistics, computer vision, exploratory multiway data analysis, blind source separation and polynomial op-timization. However, it is generally NP-hard as we know from its matrix case. To facilitate the CP tensor verification and decomposition, more properties for the CP ten-sor are further studied, and a great variety of its easily checkable subclasses such as the positive Cauchy tensors, the symmetric Pascal tensors, the Lehmer tensors, the power mean tensors, and all their nonnegative fractional Hadamard powers and Hadamard products, are exploited in this paper. Particularly, a so-called CP-Vandermonde decom-position for positive Cauchy-Hankel tensors is established and a numerical algorithm is proposed to obtain such a special type of CP decomposition. The doubly nonnegative (DNN) matrix is generalized to higher order tensors as well. Based on the DNN tensors, a series of tractable outer approximations are characterized to approximate the CP ten-sor cone, which serve as potential useful surrogates in the corresponding CP tensor cone programming arising from polynomial programming problems.
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