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

Tong Wu

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

Tong Wu

Machine Learning · Submitted 18 Jul 2023

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Finally, extensive experimental results on synthetic and real data demonstrate the effectiveness of the proposed algorithms.

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What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.15 · human participants 0.06 · controlled comparison 0.10 · randomized assignment 0.01 · states quantitative result 0.08 · compares with prior results 0.70 · mentions code or data availability 0.99.

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arXiv listing abstract v3. Results and the main claim are underlined; show every role.

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.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	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.	background 1.00	0.04	0.02	asserted 1.00
s1	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.	gap 0.89	0.06	0.03	asserted 0.99
s2	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.	contribution 0.96	0.95	0.41	asserted 1.00
s3	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.	result 0.65	0.90	0.44	asserted 1.00
s4	Moreover, an extension of OR-TLRR is proposed to handle the case when parts of the data are missing.	contribution 0.95	0.92	0.04	asserted 0.98
s5	Finally, extensive experimental results on synthetic and real data demonstrate the effectiveness of the proposed algorithms.	result 0.95	0.92	0.36	asserted 1.00
s6	We release our code at https://github.com/twugithub/2024-AISTATS-ORTLRR.	contribution 0.72	0.76	0.02	asserted 0.95

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from observation or experiment 0.44.

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Original 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.

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