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Statistics > Machine Learning
Title: Robust Data Clustering with Outliers via Transformed Tensor Low-Rank Representation
(Submitted on 18 Jul 2023 (v1), last revised 26 Apr 2024 (this version, v3))
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 this https URL
Submission history
From: Tong Wu [view email][v1] Tue, 18 Jul 2023 08:11:08 GMT (599kb)
[v2] Wed, 28 Feb 2024 12:09:34 GMT (1141kb)
[v3] Fri, 26 Apr 2024 01:29:46 GMT (1141kb)
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