The Canonical Polyadic (CP) tensor decomposition has become an attractive mathematical tool in several fields during the last ten years. This decomposition is very powerful for representing and analyzing multidimensional data. The most attractive feature of the CP decomposition is its uniqueness, contrary to rank-revealing matrix decompositions, where the problem of rotational invariance remains. This paper presents the performance analysis of iterative descent algorithms for calculating the CP decomposition of tensors when columns of factor matrices are almost collinear – i.e. swamp problems arise. We propose in this paper a new and efficient proximal algorithm based on the Forward Backward splitting method. More precisely, the existence of the best low-rank tensor approximation is ensured thanks to a coherence constraint implemented via a logarithmic regularized barrier. Computer experiments demonstrate the efficiency and stability of the proposed algorithm in comparison to other iterative algorithms in the literature for the normal case, and also producing significant results even in difficult situations.

在过去的十年中，典型多元 (CP) 张量分解已成为多个领域的有吸引力的数学工具。这种分解对于表示和分析多维数据非常有用。CP 分解最吸引人的特点是它的独特性，这与秩揭示矩阵分解相反，其中旋转不变性问题仍然存在。本文介绍了当因子矩阵的列几乎共线时（即出现沼泽问题），用于计算张量 CP 分解的迭代下降算法的性能分析。我们在本文中提出了一种基于前向后向分裂方法的新型高效近端算法。更确切地说，由于通过对数正则化障碍实现的相干约束，确保了最佳低秩张量近似的存在。计算机实验证明了与文献中的其他迭代算法相比，所提出的算法在正常情况下的效率和稳定性，即使在困难的情况下也能产生显着的结果。