# Graph Regularized Tensor Train Decomposition

arXiv: https://arxiv.org/abs/1911.01591 · HTML: https://mlsanity.com/paper/1911.01591/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Nov 2019.

## Built on by (most cited first, 4 of 4)

- [Position: Tensor Networks are a Valuable Asset for Green AI](https://mlsanity.com/paper/2205.12961/) (2022)
- [Graph-Regularized Tensor Regression: A Domain-Aware Framework for Interpretable Multi-Way Financial Modelling](https://mlsanity.com/paper/2211.05581/) (2022)
- [A Robust and Non-Iterative Tensor Decomposition Method with Automatic Thresholding](https://mlsanity.com/paper/2505.06203/) (2025)
- [Coupled Tensor-Tensor Completion Method with Applications in Drug Repurposing](https://mlsanity.com/paper/2609.03190/) (2026)

## Abstract (arXiv)

With the advances in data acquisition technology, tensor objects are collected in a variety of applications including multimedia, medical and hyperspectral imaging. As the dimensionality of tensor objects is usually very high, dimensionality reduction is an important problem. Most of the current tensor dimensionality reduction methods rely on finding low-rank linear representations using different generative models. However, it is well-known that high-dimensional data often reside in a low-dimensional manifold. Therefore, it is important to find a compact representation, which uncovers the low dimensional tensor structure while respecting the intrinsic geometry. In this paper, we propose a graph regularized tensor train (GRTT) decomposition that learns a low-rank tensor train model that preserves the local relationships between tensor samples. The proposed method is formulated as a nonconvex optimization problem on the Stiefel manifold and an efficient algorithm is proposed to solve it. The proposed method is compared to existing tensor based dimensionality reduction methods as well as tensor manifold embedding methods for unsupervised learning applications.