A sequential multilinear Nystr\"om algorithm for streaming low-rank approximation of tensors in Tucker format

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 A exclusively through random sketches of the original data, the algorithm effectively leverages structures in 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.