In this work, we propose a novel method for tensorial independent component analysis. Our approach is based on TJADE and $ k $-JADE, two recently proposed generalizations of the classical JADE algorithm. Our novel method achieves the consistency and the limiting distribution of TJADE under mild assumptions, and at the same time offers notable improvement in computational speed. Detailed mathematical proofs of the statistical properties of our method are given and, as a special case, a conjecture on the properties of $ k $-JADE is resolved. Simulations and timing comparisons demonstrate remarkable gain in speed. Moreover, the desired efficiency is obtained approximately for finite samples. The method is applied successfully to large-scale video data, for which neither TJADE nor $ k $-JADE is feasible. Finally, an experimental procedure is proposed to select the values of a set of tuning parameters.

中文翻译：

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 快速张量 JADE


在这项工作中，我们提出了一种张量独立分量分析的新方法。我们的方法基于 TJADE 和 $k$-JADE，这两个最近提出的经典 JADE 算法的推广。我们的新方法在温和的假设下实现了 TJADE 的一致性和极限分布，同时计算速度显着提高。给出了我们方法的统计特性的详细数学证明，并且作为一种特殊情况，解决了对 $ k $-JADE 特性的猜想。模拟和时序比较表明速度显着提高。此外，对于有限样本，近似获得了所需的效率。该方法成功应用于大规模视频数据，而 TJADE 和 $k$-JADE 均不可行。最后，提出了一个实验程序来选择一组调整参数的值。