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Updated: Sep 15, 2025

Diffusion Tensor Magnetic Resonance Imaging in the Analysis of Neurodegenerative Diseases

Diffusion Tensor Magnetic Resonance Imaging in the Analysis of Neurodegenerative Diseases

Published on: July 28, 2013

Tensor network decomposition for data recovery: Recent advancements and future prospects.

Yu-Bang Zheng¹, Xi-Le Zhao², Heng-Chao Li¹

¹School of Information Science and Technology, Southwest Jiaotong University, Chengdu, 611756, China.

Neural Networks : the Official Journal of the International Neural Network Society

|July 15, 2025

Summary

Tensor network (TN) decomposition is key for high-dimensional data analysis and recovery. This review details TN decomposition methods, applications, and future research directions for complex data challenges.

Keywords:

High-dimensional data analysis Image processing Low-rank modeling Tensor decomposition Tensor network

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Area of Science:

Computational Mathematics
Data Science
Quantum Information Theory

Background:

Tensor network (TN) decomposition is crucial for analyzing high-dimensional data.
Recent scholarly work highlights the growing significance of TN decomposition.
A comprehensive review of TN decomposition advancements and future prospects is lacking.

Purpose of the Study:

To provide a detailed review and discussion of tensor network decomposition.
To serve as a comprehensive resource for researchers in the field.
To catalyze future innovative breakthroughs in high-dimensional data analysis.

Main Methods:

Review of tensor concepts, operational rules, and computational properties.
Analysis of various TN decompositions, their topologies, benefits, limitations, and algorithms.
Focus on tensor network structure search (TN-SS) methods and high-dimensional data recovery.

Main Results:

Detailed explanation of TN decomposition concepts and properties.
Comparison of different TN decompositions and their associated numerical algorithms.
Evaluation of TN decomposition-based data recovery methods through numerical experiments.

Conclusions:

TN decomposition is a powerful tool for high-dimensional data recovery.
Understanding the relationship between TN ranks and matrix ranks is vital for applications.
Future research should address challenging problems and explore novel solutions in TN decomposition.