We present a sequential version of the multilinear Nystr\"om algorithm which is suitable for the low-rank Tucker approximation of tensors given in a streaming format. Accessing the tensor $\mathcal{A}$ exclusively through random sketches of the original data, the algorithm effectively leverages structures in $\mathcal{A}$, such as low-rankness, and linear combinations. We present a deterministic analysis of the algorithm and demonstrate its superior speed and efficiency in numerical experiments including an application in video processing.

翻译：本文提出一种适用于流式格式张量低秩Tucker近似的顺序多线性Nyström算法。该算法仅通过原始数据的随机草图访问张量$\mathcal{A}$，能有效利用$\mathcal{A}$中的低秩性和线性组合等结构特征。我们给出了算法的确定性分析，并通过包含视频处理应用在内的数值实验证明了其在速度与效率方面的优越性。