He is currently a postdoctoral researcher at the University of Orléans, INSA CVL, PRISME, France. He received his B.Sc. and M.Sc. degrees in Electronics and Communications from Vietnam National University Hanoi, VNU-UET, in 2016 and 2018 respectively, and his Ph.D. degree in Computer Science and Signal Processing from the University of Orléans, INSA CVL, PRISME, France in 2022. His research interests include signal processing and its applications, e.g., subspace analysis/tracking, tensor decomposition/tracking, system identification, and biomedical signal processing.

Tensor methods: Concepts, Algorithms & Applications

The era of “Big Data”, which deals with massive datasets, has brought new analysis techniques for discovering new valuable information hidden in the data. Among these techniques is multilinear low-rank approximation (LRA) of matrices and tensors, which has recently attracted a lot of attention from engineers and researchers in the signal processing and machine learning communities. A tensor is a multidimensional array and provides a natural representation of high-dimensional data. Low-rank approximation of tensors (t-LRA) can be considered as a multiway extension of LRA of matrices (which are two-way) to higher dimensions. Generally, t-LRA is referred to as tensor decomposition which allows factorizing a tensor into a sequence of basic components. As a result, t-LRA provides a useful tool for dealing with several large-scale multidimensional problems in modern data analysis which would be, otherwise, intractable by classical methods.

This lecture is a brief review of different tensor concepts and different tensor decomposition algorithms with illustrative application examples in biomedical signal processing. It is addressed to a wide audience with general background in signal processing.