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Low-tubal-rank tensor approximation has been proposed to analyze large-scaleand multi-dimensional data. However, finding such an accurate approximation ischallenging in the streaming setting, due to the limited computationalresources. To alleviate this issue, this paper extends a popular matrixsketching technique, namely Frequent Directions, for constructing an efficientand accurate low-tubal-rank tensor approximation from streaming data based onthe tensor Singular Value Decomposition (t-SVD). Specifically, the newalgorithm allows the tensor data to be observed slice by slice, but only needsto maintain and incrementally update a much smaller sketch which could capturethe principal information of the original tensor. The rigorous theoreticalanalysis shows that the approximation error of the new algorithm can bearbitrarily small when the sketch size grows linearly. Extensive experimentalresults on both synthetic and real multi-dimensional data further reveal thesuperiority of the proposed algorithm compared with other sketching algorithmsfor getting low-tubal-rank approximation, in terms of both efficiency andaccuracy.

Effective Streaming Low-tubal-rank Tensor Approximation via Frequent Directions