2020/01/20 by Salman Ahmadi‐Asl, Ahmadi-Asl, Salman, Stanislav Abukhovich +11 · 1 citation
Mathematics · #FOS: Mathematics #Numerical Analysis (math.NA) #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.2001.07124
openalex publication_date 2020/01/20 · openalex created_date 2022/07/26 · openalex updated_date 2026/08/04
Big data analysis has become a crucial part of new emerging technologies such\nas the internet of things, cyber-physical analysis, deep learning, anomaly\ndetection, etc. Among many other techniques, dimensionality reduction plays a\nkey role in such analyses and facilitates feature selection and feature\nextraction. Randomized algorithms are efficient tools for handling big data\ntensors. They accelerate decomposing large-scale data tensors by reducing the\ncomputational complexity of deterministic algorithms and the communication\namong different levels of the memory hierarchy, which is the main bottleneck in\nmodern computing environments and architectures. In this paper, we review\nrecent advances in randomization for the computation of Tucker decomposition\nand Higher Order SVD (HOSVD). We discuss random projection and sampling\napproaches, single-pass, and multi-pass randomized algorithms, and how to\nutilize them in the computation of the Tucker decomposition and the HOSVD.\nSimulations on synthetic and real datasets are provided to compare the\nperformance of some of the best and most promising algorithms.\n