Recently, there has been a trend to combine independent component analysis and canonical / parallel factor analysis (ICA-CPA) for an enhanced robustness for the computation of CPA, and ICA-CPA could be further converted into the problem of canonical polyadic decomposition (CPD) of a 5th-order partially symmetric tensor, by calculating the 4th-order cumulant of a trilinear mixture. In this study, we propose a new 5th-order CPD algorithm constrained with partial symmetry using joint diagonalization. As the main steps involved in the proposed algorithm undergo no updating iterations for the loading matrices, it is much faster than the existing algorithm based on alternating least squares and enhanced line search, and therefore could be used as a nice initialization for the latter. Simulation results are given to examine the performance of the proposed algorithm.

本研究提出了基于联合对角化的新的5阶部分对称张量约束CPD算法，与现有的基于交替最小二乘法和增强线性搜索的算法相比，本算法的主要步骤不需要更新载荷矩阵，因此速度更快，在保持良好性能的同时提高了计算CPD鲁棒性。模拟结果证明了该算法的优越性。

Fifth-order canonical polyadic decomposition with partial symmetry via
  joint diagonalization for combined independent component analysis and
  canonical / Parallel factor analysis

通过联合对角化实现独立分量分析和典范多项式分解