Robust subspace clustering via symmetry constrained latent low rank representation with converted nuclear norm

Low-rank matrix is desired in many machine learning and computer vision problems. Most of the recent studies use the nuclear norm as a convex surrogate of the rank operator. However, all singular values are simply added together by the nuclear norm, and thus the rank may not be well approximated in practical problems. In this paper, we propose using a log-determinant (LogDet) function as a smooth and closer, though nonconvex, approximation to rank for obtaining a low-rank representation in subspace clustering. Augmented Lagrange multipliers strategy is applied to iteratively optimize the LogDet-based nonconvex objective function on potentially large-scale data. By making use of the angular information of principal directions of the resultant low-rank representation, an affinity graph matrix is constructed for spectral clustering. Experimental results on motion segmentation and face clustering data demonstrate that the proposed method often outperforms state-of-the-art subspace clustering algorithms.

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Tensor-SVD Based Graph Learning for Multi-View Subspace Clustering

Proceedings of the AAAI Conference on Artificial Intelligence ◽

10.1609/aaai.v34i04.5807 ◽

2020 ◽

Vol 34 (04) ◽

pp. 3930-3937 ◽

Cited By ~ 1

Author(s):

Quanxue Gao ◽

Wei Xia ◽

Zhizhen Wan ◽

Deyan Xie ◽

Pu Zhang

Keyword(s):

Subspace Clustering ◽

Singular Values ◽

Nuclear Norm ◽

Low Rank ◽

Clustering Methods ◽

Norm Minimization ◽

Illumination Changes ◽

Low Rank Representation ◽

Value Decomposition ◽

Tensor Nuclear Norm

Low-rank representation based on tensor-Singular Value Decomposition (t-SVD) has achieved impressive results for multi-view subspace clustering, but it does not well deal with noise and illumination changes embedded in multi-view data. The major reason is that all the singular values have the same contribution in tensor-nuclear norm based on t-SVD, which does not make sense in the existence of noise and illumination change. To improve the robustness and clustering performance, we study the weighted tensor-nuclear norm based on t-SVD and develop an efficient algorithm to optimize the weighted tensor-nuclear norm minimization (WTNNM) problem. We further apply the WTNNM algorithm to multi-view subspace clustering by exploiting the high order correlations embedded in different views. Extensive experimental results reveal that our WTNNM method is superior to several state-of-the-art multi-view subspace clustering methods in terms of performance.

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Subspace clustering using a symmetric low-rank representation

Knowledge-Based Systems ◽

10.1016/j.knosys.2017.02.031 ◽

2017 ◽

Vol 127 ◽

pp. 46-57 ◽

Cited By ~ 10

Author(s):

Jie Chen ◽

Hua Mao ◽

Yongsheng Sang ◽

Zhang Yi

Keyword(s):

Subspace Clustering ◽

Low Rank ◽

Low Rank Representation

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Multiview Common Subspace Clustering via Coupled Low Rank Representation

ACM Transactions on Intelligent Systems and Technology ◽

10.1145/3465056 ◽

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.

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