# A Novel Tensor Factorization-Based Method with Robustness to Inaccurate Rank Estimation

arXiv: https://arxiv.org/abs/2305.11458 · HTML: https://mlsanity.com/paper/2305.11458/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 65 references that are in the map.
- First posted on arXiv 19 May 2023.

## Builds on (most cited first, 12 of 12)

- [DOTA: A Large-scale Dataset for Object Detection in Aerial Images](https://mlsanity.com/paper/1711.10398/) (2017)
- [GOT-10k: A Large High-Diversity Benchmark for Generic Object Tracking in the Wild](https://mlsanity.com/paper/1810.11981/) (2018)
- [Tensor Robust Principal Component Analysis with A New Tensor Nuclear Norm](https://mlsanity.com/paper/1804.03728/) (2018)
- [Exact tensor completion using t-SVD](https://mlsanity.com/paper/1502.04689/) (2015)
- [Novel methods for multilinear data completion and de-noising based on tensor-SVD](https://mlsanity.com/paper/1407.1785/) (2014)
- [Bayesian Robust Tensor Factorization for Incomplete Multiway Data](https://mlsanity.com/paper/1410.2386/) (2014)
- [Multi-dimensional imaging data recovery via minimizing the partial sum of tubal nuclear norm](https://mlsanity.com/paper/1712.05870/) (2017)
- [Low-tubal-rank Tensor Completion using Alternating Minimization](https://mlsanity.com/paper/1610.01690/) (2016)
- [Exact Low Tubal Rank Tensor Recovery from Gaussian Measurements](https://mlsanity.com/paper/1806.02511/) (2018)
- [Bilinear Factor Matrix Norm Minimization for Robust PCA: Algorithms and Applications](https://mlsanity.com/paper/1810.05186/) (2018)
- [A New Low-Rank Tensor Model for Video Completion](https://mlsanity.com/paper/1509.02027/) (2015)
- [Iterative Log Thresholding](https://mlsanity.com/paper/1312.1522/) (2013)

## Built on by (most cited first, 1 of 1)

- [Efficient Low-Tubal-Rank Tensor Estimation via Alternating Preconditioned Gradient Descent](https://mlsanity.com/paper/2512.07490/) (2025)

## Abstract (arXiv)

This study aims to solve the over-reliance on the rank estimation strategy in the standard tensor factorization-based tensor recovery and the problem of a large computational cost in the standard t-SVD-based tensor recovery. To this end, we proposes a new tensor norm with a dual low-rank constraint, which utilizes the low-rank prior and rank information at the same time. In the proposed tensor norm, a series of surrogate functions of the tensor tubal rank can be used to achieve better performance in harness low-rankness within tensor data. It is proven theoretically that the resulting tensor completion model can effectively avoid performance degradation caused by inaccurate rank estimation. Meanwhile, attributed to the proposed dual low-rank constraint, the t-SVD of a smaller tensor instead of the original big one is computed by using a sample trick. Based on this, the total cost at each iteration of the optimization algorithm is reduced to O(n3log n +kn3) from O(n4) achieved with standard methods, where k is the estimation of the true tensor rank and far less than n. Our method was evaluated on synthetic and real-world data, and it demonstrated superior performance and efficiency over several existing state-of-the-art tensor completion methods.