Tensor ring (TR) decomposition is an efficient approach to discover the hidden low-rank patterns for higher-order tensors, and streaming tensors are becoming highly prevalent in real-world applications. In this paper, we investigate how to track TR decompositions of streaming tensors. An efficient algorithm is first proposed. Then, based on this algorithm and randomized techniques, we present a randomized streaming TR decomposition. The proposed algorithms make full use of the structure of TR decomposition, and the randomized version can allow any sketching type. Theoretical results on sketch size are provided. In addition, the complexity analyses for the obtained algorithms are also given. We compare our proposals with the existing batch methods using both real and synthetic data. Numerical results show that they have better performance in computing time with maintaining similar accuracy.

翻译：张量环（TR）分解是发现高阶张量中隐含低秩模式的有效方法，而流式张量在实际应用中正变得日益普遍。本文研究了如何跟踪流式张量的张量环分解。首先提出一种高效算法，随后基于该算法与随机化技术，我们提出一种随机化流式张量环分解方法。所提算法充分利用了张量环分解的结构特性，其随机化版本能够兼容任意草图化类型。本文给出了关于草图尺寸的理论结果，并提供了所获算法的复杂度分析。我们利用真实数据与合成数据将所提方法与现有批量方法进行对比，数值结果表明，在保持相近精度的同时，所提方法在计算时间上具有更优性能。