Randomized algorithms are efficient techniques for big data tensor analysis. In this tutorial paper, we review and extend a variety of randomized algorithms for decomposing large-scale data tensors in Tensor Ring (TR) format. We discuss both adaptive and nonadaptive randomized algorithms for this task. Our main focus is on the random projection technique as an efficient randomized framework and how it can be used to decompose large-scale data tensors in the TR format. Simulations are provided to support the presentation and efficiency, and performance of the presented algorithms are compared.

中文翻译：

---

快速计算低秩张量环模型的随机算法

随机算法是大数据张量分析的有效技术。在本教程文件中，我们回顾并扩展了多种用于分解张量环（TR）格式的大规模数据张量的随机算法。我们讨论了用于此任务的自适应和非自适应随机算法。我们的主要重点是作为一种有效的随机框架的随机投影技术，以及如何将其用于分解TR格式的大规模数据张量。提供了仿真以支持表示和效率，并且比较了所提出算法的性能。