Robust Subspace Clustering With Low-Rank Structure Constraint

Nie, Feiping; Chang, Wei; Hu, Zhanxuan; Li, Xuelong

doi:10.1109/tkde.2020.2995896

Cited by 27 publications

(18 citation statements)

References 37 publications

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“…That is, rank( X i ) can be rewritten as rank( X I i ). We can get the clustering label in one step by directly optimizing I i [ 28 ].…”

Section: Methodsmentioning

confidence: 99%

“…Following 0 < k ≤ 1, ‖ G ‖ S p p =Tr(( G T G ) p /2 ) [ 28 ] and Lemma 1 , the first term in equation ( 7 ) can be denoted as ∑ i =1 c Tr( I i ( A T A ) k )=∑ i =1 c (‖ A I i ‖ S p k ) 2 since I i | i =1 c ⊆{0,1} n × n . According to ∑ i =1 c I i = I , we convert the first term in equation ( 7 ) to

…”

Section: Methodsmentioning

confidence: 99%

“…When the data are clean, i.e., the samples can be strictly drawn from multiple subspaces, several existing methods, such as sparse subspace clustering (SSC) [ 27 ], low-rank representation (LRR) [ 5 ], and low-rank model with discrete group structure constraint (LRS) [ 28 ], are able to solve the subspace clustering problem. SSC clusters the data drawn from multiple low-dimensional subspaces based on sparse representation (SR) [ 29 ].…”

Section: Introductionmentioning

confidence: 99%

“…As a result, multiple low-rank subspaces can be obtained clearly. Furthermore, Nie et al introduced a piecewise function to relax the rank constraint which makes LRS better at handling the noisy dataset than the preliminary version [ 32 ].…”

Section: Introductionmentioning

confidence: 99%

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One‐Step Robust Low‐Rank Subspace Segmentation for Tumor Sample Clustering

Liu

Cheng

Wang

et al. 2021

Computational Intelligence and Neuroscience

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Clustering of tumor samples can help identify cancer types and discover new cancer subtypes, which is essential for effective cancer treatment. Although many traditional clustering methods have been proposed for tumor sample clustering, advanced algorithms with better performance are still needed. Low-rank subspace clustering is a popular algorithm in recent years. In this paper, we propose a novel one-step robust low-rank subspace segmentation method (ORLRS) for clustering the tumor sample. For a gene expression data set, we seek its lowest rank representation matrix and the noise matrix. By imposing the discrete constraint on the low-rank matrix, without performing spectral clustering, ORLRS learns the cluster indicators of subspaces directly, i.e., performing the clustering task in one step. To improve the robustness of the method, capped norm is adopted to remove the extreme data outliers in the noise matrix. Furthermore, we conduct an efficient solution to solve the problem of ORLRS. Experiments on several tumor gene expression data demonstrate the effectiveness of ORLRS.

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“…That is, rank( X i ) can be rewritten as rank( X I i ). We can get the clustering label in one step by directly optimizing I i [ 28 ].…”

Section: Methodsmentioning

confidence: 99%

…”

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

One‐Step Robust Low‐Rank Subspace Segmentation for Tumor Sample Clustering

Liu

Cheng

Wang

et al. 2021

Computational Intelligence and Neuroscience

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“…Basically, it aims to group the data points into different clusters according to their similarities or densities ( Ubukata, 2019 ; Ren, Zhang & Zhang, 2019 ). Over the past decades, a number of clustering algorithms have been proposed such as the K means clustering, spectral clustering ( Ng, Jordan & Weiss, 2001 ), min-max cut ( Ding et al, 2001 ; Nie et al, 2010 ), subspace clustering ( Nie & Huang, 2016 ; Xie et al, 2020 ), and multi-view clustering ( Nie, Tian & Li, 2018 ; Cai et al, 2013 ). Among the existing clustering methods, the most popular one is the K means clustering algorithm due to its simpleness and efficiency, which aims to learn certain cluster centroids to minimize the within cluster data distances.…”

Section: Introductionmentioning

confidence: 99%

A new Kmeans clustering model and its generalization achieved by joint spectral embedding and rotation

Huang

Peng

et al. 2021

PeerJ Computer Science

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The Kmeans clustering and spectral clustering are two popular clustering methods for grouping similar data points together according to their similarities. However, the performance of Kmeans clustering might be quite unstable due to the random initialization of the cluster centroids. Generally, spectral clustering methods employ a two-step strategy of spectral embedding and discretization postprocessing to obtain the cluster assignment, which easily lead to far deviation from true discrete solution during the postprocessing process. In this paper, based on the connection between the Kmeans clustering and spectral clustering, we propose a new Kmeans formulation by joint spectral embedding and spectral rotation which is an effective postprocessing approach to perform the discretization, termed KMSR. Further, instead of directly using the dot-product data similarity measure, we make generalization on KMSR by incorporating more advanced data similarity measures and call this generalized model as KMSR-G. An efficient optimization method is derived to solve the KMSR (KMSR-G) model objective whose complexity and convergence are provided. We conduct experiments on extensive benchmark datasets to validate the performance of our proposed models and the experimental results demonstrate that our models perform better than the related methods in most cases.

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Subspace Clustering via Integrating Sparse Representation and Adaptive Graph Learning

Deng

Huang

et al. 2021

Neural Process Lett

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Sparse representation is a powerful tool for subspace clustering, but most existing methods for this issue ignore the local manifold information in learning procedure. To this end, in this paper we propose a novel model, dubbed Sparse Representation with Adaptive Graph (SRAG), which integrates adaptive graph learning and sparse representation into a unified framework. Specifically, the former can preserve the local manifold structure of data, while the latter is useful for digging global information. For the objective function of SRAG has multiple intractable terms, an ADMM method is developed to solve it. Numerous experimental results demonstrate that our proposed method consistently outperforms several representative clustering algorithms by significant margins.

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Robust Subspace Clustering With Low-Rank Structure Constraint

Cited by 27 publications

References 37 publications

One‐Step Robust Low‐Rank Subspace Segmentation for Tumor Sample Clustering

One‐Step Robust Low‐Rank Subspace Segmentation for Tumor Sample Clustering

A new Kmeans clustering model and its generalization achieved by joint spectral embedding and rotation

Subspace Clustering via Integrating Sparse Representation and Adaptive Graph Learning

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