Exploiting Commutativity Condition for CP Decomposition Via Approximate Simultaneous Diagonalization
Exploiting Commutativity Condition for CP Decomposition Via Approximate Simultaneous Diagonalization
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DOI：
10.1109/icassp40776.2020.9054027
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发表时间：
2020-05
期刊：
影响因子：
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通讯作者：
Riku Akema;M. Yamagishi;I. Yamada
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文献类型：
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作者：
Riku Akema;M. Yamagishi;I. Yamada
在本文中，我们提出了一种新的战略，利用了固有的代数性质的同时对角化矩阵元组，即，交换性，用于（i）将高阶张量的近似CP分解减少到近似同时对角化（ASD）和（ii）求解ASD。通过使用交换性准则，我们设计了一个矩阵元组与给定张量的矩阵切片。然后，对于所设计元组的ASD，我们使用近似然后对角化同时（ATDS）算法，该算法利用交换性来求解ASD。数值实验表明，所提出的策略取得了更好的性能比传统的，特别是当矩阵估计几乎共线列。
In this paper, we propose a novel strategy which utilizes an inherent algebraic property of simultaneously diagonalizable matrix tuples, i.e., commutativity, for both (i) reducing approximate CP decomposition of a higher-order tensor to Approximate Simultaneous Diagonalization (ASD) and (ii) solving the ASD. By using a commutativity criterion, we design a matrix tuple with matrix slices of a given tensor. Then, for the ASD of the designed tuple, we use the Approximate-Then-Diagonalize-Simultaneously (ATDS) algorithm which utilizes commutativity to solve ASD. Numerical experiments show that the proposed strategy achieves better performance than conventional ones particularly when matrices to be estimated has almost collinear columns.