# Performance of Rank-One Tensor Approximation on Incomplete Data

arXiv: https://arxiv.org/abs/2504.07818 · HTML: https://mlsanity.com/paper/2504.07818/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 7 references that are in the map.
- First posted on arXiv 10 Apr 2025.

## Builds on (most cited first, 4 of 4)

- [Tensor Decomposition for Signal Processing and Machine Learning](https://mlsanity.com/paper/1607.01668/) (2016)
- [When Random Tensors meet Random Matrices](https://mlsanity.com/paper/2112.12348/) (2021)
- [Two-way kernel matrix puncturing: towards resource-efficient PCA and spectral clustering](https://mlsanity.com/paper/2102.12293/) (2021)
- [A Random Matrix Approach to Low-Multilinear-Rank Tensor Approximation](https://mlsanity.com/paper/2402.03169/) (2024)

## Abstract (arXiv)

We are interested in the estimation of a rank-one tensor signal when only a portion varepsilon of its noisy observation is available. We show that the study of this problem can be reduced to that of a random matrix model whose spectral analysis gives access to the reconstruction performance. These results shed light on and specify the loss of performance induced by an artificial reduction of the memory cost of a tensor via the deletion of a random part of its entries.