A closed-form solution for multilinear PARAFAC decompositions
A closed-form solution for multilinear PARAFAC decompositions
复制标题
多线性 PARAFAC 分解的闭式解
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
M. Haardt
中科院分区：
文献类型：
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作者：
F. Roemer;M. Haardt
在本文中，我们研究 R 路并行因子分析（也称为 R 路 PARAFAC）问题。多路信号处理的这一分支最近受到了越来越多的关注，这是由于该模型的多功能性以及可识别性结果证明了其相对于纯矩阵（2 路）方法的优越性。在 R 路 PARAFAC 分析中，目标是将 R 维张量分解为 1 阶项的最小和。到目前为止，存在次优封闭式解决方案以及用于查找这些分解的迭代技术。然而，后者通常需要多次迭代才能收敛。在这篇文章中，我们证明了 R 路 PARAFAC 分解可以简化为一组同时矩阵对角化问题。利用 R 维问题的结构，我们获得每个因素的多个估计，并提出一个“最佳匹配”方案来为每个因素选择最佳估计。通过计算机模拟，我们将封闭式解决方案与迭代技术进行比较，并证明在关键场景中增强的鲁棒性。
In this paper we study the R-way Parallel Factor Analysis (also referred to as R-way PARAFAC) problem. This branch of multi-way signal processing has received increased attention recently which is due to the versatility of the model as well as the identifiability results demonstrating its superiority to matrix-only (2-way) approaches. In R-way PARAFAC analysis, the goal is to decompose an R-dimensional tensor into a minimal sum of rank-1 terms. So far, there exist sub-optimal closed-form solutions as well as iterative techniques for finding these decompositions. However, the latter often require many iterations to converge. In this contribution we demonstrate that the R-way PARAFAC decomposition can be reduced to a set of simultaneous matrix diagonalization problems. Exploiting the structure of the R-dimensional problem, we obtain several estimates for each of the factors and present a "best matching" scheme to select the best estimate for each factor. By means of computer simulations we compare our closed-form solution to an iterative technique and demonstrate the enhanced robustness in critical scenarios.