# Fast Robust Tensor Principal Component Analysis via Fiber CUR Decomposition

arXiv: https://arxiv.org/abs/2108.10448 · HTML: https://mlsanity.com/paper/2108.10448/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 35 references that are in the map.
- First posted on arXiv 23 Aug 2021.

## Builds on (most cited first, 10 of 10)

- [Tensor Robust Principal Component Analysis with A New Tensor Nuclear Norm](https://mlsanity.com/paper/1804.03728/) (2018)
- [Novel methods for multilinear data completion and de-noising based on tensor-SVD](https://mlsanity.com/paper/1407.1785/) (2014)
- [Non-convex Robust PCA](https://mlsanity.com/paper/1410.7660/) (2014)
- [Robust Low-rank Tensor Recovery: Models and Algorithms](https://mlsanity.com/paper/1311.6182/) (2013)
- [Accelerated Alternating Projections for Robust Principal Component Analysis](https://mlsanity.com/paper/1711.05519/) (2017)
- [Robust CUR Decomposition: Theory and Imaging Applications](https://mlsanity.com/paper/2101.05231/) (2021)
- [Rapid Robust Principal Component Analysis: CUR Accelerated Inexact Low Rank Estimation](https://mlsanity.com/paper/2010.07422/) (2020)
- [Mode-wise Tensor Decompositions: Multi-dimensional Generalizations of CUR Decompositions](https://mlsanity.com/paper/2103.11037/) (2021)
- [Robust Tensor Recovery with Fiber Outliers for Traffic Events](https://mlsanity.com/paper/1908.10198/) (2019)
- [Tensor vs Matrix Methods: Robust Tensor Decomposition under Block Sparse Perturbations](https://mlsanity.com/paper/1510.04747/) (2015)

## Built on by (most cited first, 8 of 8)

- [Learned Robust PCA: A Scalable Deep Unfolding Approach for High-Dimensional Outlier Detection](https://mlsanity.com/paper/2110.05649/) (2021)
- [Matrix Completion with Cross-Concentrated Sampling: Bridging Uniform Sampling and CUR Sampling](https://mlsanity.com/paper/2208.09723/) (2022)
- [Robust Tensor CUR Decompositions: Rapid Low-Tucker-Rank Tensor Recovery with Sparse Corruption](https://mlsanity.com/paper/2305.04080/) (2023)
- [Riemannian CUR Decompositions for Robust Principal Component Analysis](https://mlsanity.com/paper/2206.09042/) (2022)
- [On the Robustness of Cross-Concentrated Sampling for Matrix Completion](https://mlsanity.com/paper/2401.15566/) (2024)
- [Error Analysis of Tensor-Train Cross Approximation](https://mlsanity.com/paper/2207.04327/) (2022)
- [Hyperspectral Band Selection based on Generalized 3DTV and Tensor CUR Decomposition](https://mlsanity.com/paper/2405.00951/) (2024)
- [Property Inheritance for Subtensors in Tensor Train Decompositions](https://mlsanity.com/paper/2504.11396/) (2025)

## Abstract (arXiv)

We study the problem of tensor robust principal component analysis (TRPCA), which aims to separate an underlying low-multilinear-rank tensor and a sparse outlier tensor from their sum. In this work, we propose a fast non-convex algorithm, coined Robust Tensor CUR (RTCUR), for large-scale TRPCA problems. RTCUR considers a framework of alternating projections and utilizes the recently developed tensor Fiber CUR decomposition to dramatically lower the computational complexity. The performance advantage of RTCUR is empirically verified against the state-of-the-arts on the synthetic datasets and is further demonstrated on the real-world application such as color video background subtraction.