scholarly journals Subspace clustering using a symmetric low-rank representation

2017 ◽  
Vol 127 ◽  
pp. 46-57 ◽  
Author(s):  
Jie Chen ◽  
Hua Mao ◽  
Yongsheng Sang ◽  
Zhang Yi
Keyword(s):  
Subspace Clustering ◽  
Low Rank ◽  
Low Rank Representation

Multiview Common Subspace Clustering via Coupled Low Rank Representation

2021 ◽  
Vol 12 (4) ◽  
pp. 1-25
Author(s):  
Stanley Ebhohimhen Abhadiomhen ◽  
Zhiyang Wang ◽  
Xiangjun Shen ◽  
Jianping Fan
Keyword(s):  
Common Knowledge ◽  
Subspace Clustering ◽  
Laplacian Matrix ◽  
Low Rank ◽  
Connected Components ◽  
Similarity Matrix ◽  
Benchmark Datasets ◽  
Low Rank Representation ◽  
Low Dimensional ◽  
Shared Structure

Multi-view subspace clustering (MVSC) finds a shared structure in latent low-dimensional subspaces of multi-view data to enhance clustering performance. Nonetheless, we observe that most existing MVSC methods neglect the diversity in multi-view data by considering only the common knowledge to find a shared structure either directly or by merging different similarity matrices learned for each view. In the presence of noise, this predefined shared structure becomes a biased representation of the different views. Thus, in this article, we propose a MVSC method based on coupled low-rank representation to address the above limitation. Our method first obtains a low-rank representation for each view, constrained to be a linear combination of the view-specific representation and the shared representation by simultaneously encouraging the sparsity of view-specific one. Then, it uses the k -block diagonal regularizer to learn a manifold recovery matrix for each view through respective low-rank matrices to recover more manifold structures from them. In this way, the proposed method can find an ideal similarity matrix by approximating clustering projection matrices obtained from the recovery structures. Hence, this similarity matrix denotes our clustering structure with exactly k connected components by applying a rank constraint on the similarity matrix’s relaxed Laplacian matrix to avoid spectral post-processing of the low-dimensional embedding matrix. The core of our idea is such that we introduce dynamic approximation into the low-rank representation to allow the clustering structure and the shared representation to guide each other to learn cleaner low-rank matrices that would lead to a better clustering structure. Therefore, our approach is notably different from existing methods in which the local manifold structure of data is captured in advance. Extensive experiments on six benchmark datasets show that our method outperforms 10 similar state-of-the-art compared methods in six evaluation metrics.

Non-convex low-rank representation combined with rank-one matrix sum for subspace clustering

2020 ◽  
Vol 24 (20) ◽  
pp. 15317-15326
Author(s):  
Xiaofang Liu ◽  
Jun Wang ◽  
Dansong Cheng ◽  
Daming Shi ◽  
Yongqiang Zhang
Keyword(s):  
Subspace Clustering ◽  
Low Rank ◽  
Rank One ◽  
Low Rank Representation

Low-rank representation with graph regularization for subspace clustering

2015 ◽  
Vol 21 (6) ◽  
pp. 1569-1581 ◽  
Author(s):  
Wu He ◽  
Jim X. Chen ◽  
Weihua Zhang
Keyword(s):  
Subspace Clustering ◽  
Low Rank ◽  
Graph Regularization ◽  
Low Rank Representation
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