  Big data analysis has become a crucial part of new emerging technologies such
as the internet of things, cyber-physical analysis, deep learning, anomaly
detection, etc. Among many other techniques, dimensionality reduction plays a
key role in such analyses and facilitates feature selection and feature
extraction. Randomized algorithms are efficient tools for handling big data
tensors. They accelerate decomposing large-scale data tensors by reducing the
computational complexity of deterministic algorithms and the communication
among different levels of the memory hierarchy, which is the main bottleneck in
modern computing environments and architectures. In this paper, we review
recent advances in randomization for the computation of Tucker decomposition
and Higher Order SVD (HOSVD). We discuss random projection and sampling
approaches, single-pass, and multi-pass randomized algorithms, and how to
utilize them in the computation of the Tucker decomposition and the HOSVD.
Simulations on synthetic and real datasets are provided to compare the
performance of some of the best and most promising algorithms.
