# Robust Data Clustering with Outliers via Transformed Tensor Low-Rank Representation

arXiv: https://arxiv.org/abs/2307.09055 · HTML: https://mlsanity.com/paper/2307.09055/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 51 references that are in the map.
- First posted on arXiv 18 Jul 2023.

## Builds on (most cited first, 14 of 14)

- [Unsupervised Deep Embedding for Clustering Analysis](https://mlsanity.com/paper/1511.06335/) (2015)
- [Invariant Information Clustering for Unsupervised Image Classification and Segmentation](https://mlsanity.com/paper/1807.06653/) (2018)
- [Contrastive Clustering](https://mlsanity.com/paper/2009.09687/) (2020)
- [Tensor Robust Principal Component Analysis with A New Tensor Nuclear Norm](https://mlsanity.com/paper/1804.03728/) (2018)
- [Deep Subspace Clustering Networks](https://mlsanity.com/paper/1709.02508/) (2017)
- [Scalable Sparse Subspace Clustering by Orthogonal Matching Pursuit](https://mlsanity.com/paper/1507.01238/) (2015)
- [Subspace Clustering by Block Diagonal Representation](https://mlsanity.com/paper/1805.09243/) (2018)
- [Framelet Representation of Tensor Nuclear Norm for Third-Order Tensor Completion](https://mlsanity.com/paper/1909.06982/) (2019)
- [On Unifying Multi-View Self-Representations for Clustering by Tensor Multi-Rank Minimization](https://mlsanity.com/paper/1610.07126/) (2016)
- [Dictionary Learning with Low-rank Coding Coefficients for Tensor Completion](https://mlsanity.com/paper/2009.12507/) (2020)
- [Exact Low Tubal Rank Tensor Recovery from Gaussian Measurements](https://mlsanity.com/paper/1806.02511/) (2018)
- [Subspace Learning and Imputation for Streaming Big Data Matrices and Tensors](https://mlsanity.com/paper/1404.4667/) (2014)
- [Tensor Q-Rank: New Data Dependent Definition of Tensor Rank](https://mlsanity.com/paper/1910.12016/) (2019)
- [Clustering multi-way data: a novel algebraic approach](https://mlsanity.com/paper/1412.7056/) (2014)

## Abstract (arXiv)

Recently, tensor low-rank representation (TLRR) has become a popular tool for tensor data recovery and clustering, due to its empirical success and theoretical guarantees. However, existing TLRR methods consider Gaussian or gross sparse noise, inevitably leading to performance degradation when the tensor data are contaminated by outliers or sample-specific corruptions. This paper develops an outlier-robust tensor low-rank representation (OR-TLRR) method that provides outlier detection and tensor data clustering simultaneously based on the t-SVD framework. For tensor observations with arbitrary outlier corruptions, OR-TLRR has provable performance guarantee for exactly recovering the row space of clean data and detecting outliers under mild conditions. Moreover, an extension of OR-TLRR is proposed to handle the case when parts of the data are missing. Finally, extensive experimental results on synthetic and real data demonstrate the effectiveness of the proposed algorithms. We release our code at https://github.com/twugithub/2024-AISTATS-ORTLRR.