Tensor Decomposition for Medicine

Tensor decomposition (TD) is a powerful mathematical framework for analyzing high-dimensional and multi-way data, such as medical images, biomedical signals, and clinical measurements. Unlike conventional matrix-based methods, TD represents a tensor as a combination of lower-dimensional factor matrices or core tensors, enabling the extraction of latent structures while preserving the intrinsic multi-dimensional relationships within the data.

In medicine, many datasets (e.g., MRI, PET, CT, EGG, EMG ) can be naturally exhibited as a tensor structure. For example, medical imaging data can be organized according to spatial dimensions, time, imaging modality, or patients, while physiological signals may involve multiple subjects, channels, and temporal measurements. Tensor decomposition can therefore provide compact representations, reduce computational and storage costs, and facilitate the discovery of meaningful patterns and biomarkers.

Selected Publications

L.T. Thanh, K. Abed-Meraim, N.L. Trung, P. Ravier, O. Buttelli, A. Holobar. Tensor-based Higher-Order Multivariate Singular Spectrum Analysis and Applications to Multichannel Biomedical Signal Analysis. Signal Processing, 2025.

L.T. Thanh, K. Abed-Meraim, N.L. Trung. Higher-Order Singular Spectrum Analysis For Multichannel Biomedical Signal Analysis. European Signal Processing Conference (EUSIPCO), 2024.

Le Trung Thanh, Nguyen Thi Anh Dao, Nguyen Viet Dung, Nguyen Linh Trung, and Karim Abed-Meraim. Multi-channel EEG epileptic spike detection by a new method of tensor decomposition. IOP Journal of Neural Engineering, 17(1):016023, January 2020.

Nguyen Thi Anh-Dao, Le Trung Thanh, Nguyen Linh-Trung, and Ha Vu Le. Nonnegative tensor decomposition for EEG epileptic spike detection. NAFOSTED Conference on Information and Computer Science (NICS), pages 196–201, Hanoi, Vietnam, November 2018. [Best paper award].

Nguyen Linh-Trung, Truong Minh-Chinh, Viet-Dung Nguyen, and Karim Abed-Meraim. A non-linear tensor tracking algorithm for analysis of incomplete multi-channel EEG data. 12th International Symposium on Medical Information and Communication Technology (ISMICT), pages 114–119, Sydney, Australia, March 2018.