A sequential multilinear Nyström algorithm for streaming low-rank approximation of tensors in Tucker format

Abstract

We present a sequential version of the multilinear Nyström algorithm which is suitable for 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.