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

TL;DR

This paper introduces OR-TLRR, a robust tensor low-rank representation method that effectively detects outliers and clusters tensor data, even with missing entries, outperforming existing approaches.

Contribution

The paper proposes a novel outlier-robust tensor low-rank representation method based on t-SVD, with theoretical guarantees and extensions for missing data.

Findings

Proves exact recovery of clean data row space under mild conditions.

Successfully detects outliers in tensor data with arbitrary corruptions.

Demonstrates superior performance on synthetic and real datasets.

Abstract

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.