# Structured Low-Rank Tensor Learning

arXiv: https://arxiv.org/abs/2305.07967 · HTML: https://mlsanity.com/paper/2305.07967/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 42 references that are in the map.
- First posted on arXiv 13 May 2023.

## Builds on (most cited first, 5 of 5)

- [Low-Rank Hankel Tensor Completion for Traffic Speed Estimation](https://mlsanity.com/paper/2105.11335/) (2021)
- [Low-rank tensor completion: a Riemannian manifold preconditioning approach](https://mlsanity.com/paper/1605.08257/) (2016)
- [Missing Slice Recovery for Tensors Using a Low-rank Model in Embedded Space](https://mlsanity.com/paper/1804.01736/) (2018)
- [Hankel Matrix Nuclear Norm Regularized Tensor Completion for N-dimensional Exponential Signals](https://mlsanity.com/paper/1604.02100/) (2016)
- [Multithreaded Filtering Preconditioner for Diffusion Equation on Structured Grid](https://mlsanity.com/paper/1909.09771/) (2019)

## Abstract (arXiv)

We consider the problem of learning low-rank tensors from partial observations with structural constraints, and propose a novel factorization of such tensors, which leads to a simpler optimization problem. The resulting problem is an optimization problem on manifolds. We develop first-order and second-order Riemannian optimization algorithms to solve it. The duality gap for the resulting problem is derived, and we experimentally verify the correctness of the proposed algorithm. We demonstrate the algorithm on nonnegative constraints and Hankel constraints.