ParaTuck-2张量分解的提升方法
A lifting approach to ParaTuck-2 tensor decompositions
AI总结：
本文提出一种提升方法，将ParaTuck-2张量分解问题转化为矩阵零空间和特征值计算，从而在已知最优唯一性条件下用代数算法精确求解PT2D及其对称版本DEDICOM，并推广到PARAFAC2分解。
摘要：
三阶张量的ParaTuck-2分解（PT2D）是著名的规范多元分解（CPD）的两层推广。虽然PT2D比CPD更具灵活性，但它也具有类似的唯一性性质。在本文中，我们证明在已知最优唯一性条件下，精确的PT2D可以通过代数算法计算（即PT2D问题可以归结为计算某些矩阵的零空间和特征值）。我们通过将张量的切片提升到高维空间来实现这一点，这也使得现有唯一性条件得以改进。所提出的算法针对一般PT2D及其对称版本（DEDICOM）开发，从而为CPD的另一种推广——PARAFAC2分解——导出了代数算法。数值实验表明，我们的方法也适用于近似场景。
英文摘要：
The ParaTuck-2 decomposition (PT2D) of third-order tensor is a two-layer generalization of the well-known canonical polyadic decomposition (CPD).While being more flexible than the CPD, the PT2D also possesses similar uniqueness properties.In this paper, we show than under the best known uniqueness conditions, the exact PT2D can be computed by an algebraic algorithm (i.e., can the PT2D problems can be reduced to computing nullspaces and eigenvalues of certain matrices).We do so by lifting the slices of the tensor to higher-dimensional space, which also allows for refining the existing uniqueness conditions.The algorithms are developed for general PT2D and its symmetric version (DEDICOM), which leads to an algebraic algorithm for another generalization of the CPD, the PARAFAC2 decomposition.Our methods are also applicable in the approximation scenario, as shown by the numerical experiments.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
