Low-Rank Tucker Approximation of a Tensor from Streaming Data

This paper describes a new algorithm for computing a low-Tucker-rank approximation of a tensor. The method applies a randomized linear map to the tensor to obtain a sketch that captures the important directions within each mode, as well as the interactions among the modes. The sketch can be extracted from streaming or distributed data or with a single pass over the tensor, and it uses storage proportional to the degrees of freedom in the output Tucker approximation. The algorithm does not require a second pass over the tensor, although it can exploit another view to compute a superior approximation. The paper provides a rigorous theoretical guarantee on the approximation error. Extensive numerical experiments show that the algorithm produces useful results that improve on the state-of-the-art for streaming Tucker decomposition.