Robust Subspace Clustering

By M. Soltanolkotabi, Ehsan Elhamifar, E.J. Candes. arXiv.org, 2013

376 citations recorded by the source corpus.

Subspace clustering refers to the task of nding a multi-subspace representation that best ts a collection of points taken from a high-dimensional space. This paper introduces an algorithm inspired by sparse subspace clustering (SSC) (25) to cluster noisy data, and develops some novel theory demonstrating its correctness. In particular, the theory uses ideas from geometric functional analysis to show that the algorithm can accurately recover the underlying subspaces under minimal requirements on their orientation, and on the number of samples per subspace. Synthetic as well as real data experiments complement our theoretical study, illustrating our approach and demonstrating its eectiveness.

Subfields: Artificial Intelligence, Computational Mechanics, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/6b2266474b2b5e9ec59f6395ed78035a7e5a3d4d

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Jiashi Feng
2. Shuicheng Yan
3. Tao Mei
4. Lei Zhang
5. Dacheng Tao
6. Wangmeng Zuo
7. René Vidal
8. Zhouchen Lin

In Computational Mechanics

1. Lei Zhang
2. Wangmeng Zuo
3. Zhouchen Lin
4. Xiangchu Feng
5. René Vidal
6. Shuicheng Yan
7. Shuhang Gu
8. Jiashi Feng

In Computer Vision and Pattern Recognition

1. Luc Van Gool
2. Lei Zhang
3. Dacheng Tao
4. Wangmeng Zuo
5. Ming-Hsuan Yang
6. Shuicheng Yan
7. Jiashi Feng
8. Yi Yang

Citations in the corpus

• Generalized Low Rank Models (2014, methodology): “Similarly, robust subspace clustering [132] can be obtained by using an `1 or Huber penalty in the subspace clustering problem.”
• Differentially private subspace clustering (2015, background): “Such settings were extensively investigated in previous development of subspace clustering algorithms [24, 25, 14].”
• Projective dictionary pair learning for pattern classification (2014, background): “Recent studies on sparse subspace clustering [19] have proved that a sample can be represented by its corresponding dictionary if the signals satisfy certain incoherence condition.”
• Low rank subspace clustering (LRSC) (2014, background): “1We refer the reader to Soltanolkotabi et al. (2013) for very recent results in this direction.”
• Scalable Sparse Subspace Clustering by Orthogonal Matching Pursuit (2015, result): “In particular, our result for deterministic arbitrary models is much stronger than the main result in [40].”
• Big data for cyber physical systems in industry 4.0: a survey (2019, methodology): “The typical methods in this type include GPCA (Vidal, Ma, and Sastry 2005), SSC (Elhamifar and Vidal 2013), and RSC (Soltanolkotabi, Elhamifar, and Candes 2014).”
• Robust continuous clustering (2017, background): “Significant advances in the last two decades include spectral clustering (2–4), generalizations of classic center-based methods (5, 6), mixture models (7, 8), mean shift (9), affinity propagation (10), subspace clustering (11–13), nonparametric methods (14, 15), and feature selection (16–20).”
• Curriculum Dropout (2017, background): “Despite the overall idea of an adaptive selection of parameters is not novel for either regularization theory [12, 7, 4, 24, 6] or tuning of network hyper-parameters (e.g. learning rate, [5]), to the best of our knowledge, this is the first time that this concept of time-adaptive regularization is…”
• Subspace Clustering by Block Diagonal Representation (2018, background): “Beyond the independent subspaces assumption, some other subspaces assumptions are proposed to analyze the block diagonal property in different settings [10], [34], [35], [41], [42].”