Provable Subspace Clustering: When LRR Meets SSC

Wang, Yu-Xiang; Xu, Huan; Leng, Chenlei

doi:10.1109/tit.2019.2915593

Cited by 79 publications

(85 citation statements)

References 41 publications

(49 reference statements)

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“…This problem can be solved efficiently using ADMM optimization procedure [11], [65]. Low-Rank Sparse Subspace Clustering (LRSSC) [29] requires that the representation matrix C is simultaneously lowrank and sparse. LRSSC solves the following problem: (9) where λ and τ are rank and sparsity regularization constants, respectively.…”

Section: A Related Workmentioning

confidence: 99%

$\ell_0$ -Motivated Low-Rank Sparse Subspace Clustering

Brbić

Kopriva

2020

IEEE Trans. Cybern.

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In many applications, high-dimensional data points can be well represented by low-dimensional subspaces. To identify the subspaces, it is important to capture a global and local structure of the data which is achieved by imposing low-rank and sparseness constraints on the data representation matrix. In low-rank sparse subspace clustering (LRSSC), nuclear and 1 norms are used to measure rank and sparsity. However, the use of nuclear and 1 norms leads to an overpenalized problem and only approximates the original problem. In this paper, we propose two 0 quasi-norm based regularizations. First, the paper presents regularization based on multivariate generalization of minimax-concave penalty (GMC-LRSSC), which contains the global minimizers of 0 quasi-norm regularized objective. Afterward, we introduce the Schatten-0 (S 0 ) and 0 regularized objective and approximate the proximal map of the joint solution using a proximal average method (S 0 / 0 -LRSSC). The resulting nonconvex optimization problems are solved using alternating direction method of multipliers with established convergence conditions of both algorithms. Results obtained on synthetic and four real-world datasets show the effectiveness of GMC-LRSSC and S 0 / 0 -LRSSC when compared to state-of-the-art methods.

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Section: A Related Workmentioning

confidence: 99%

$\ell_0$ -Motivated Low-Rank Sparse Subspace Clustering

Brbić

Kopriva

2020

IEEE Trans. Cybern.

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“…Neither a sparse nor dense similarity matrix reveals a comprehensive correlation structure among samples due to their conflicted nature [49], [50], [51]. Consequently, to achieve trade-off between sparsity and the grouping effect, numerous mixed norms, e.g., trace Lasso [52] and elastic net [33], have been integrated into the optimization function.…”

Section: A Calculating Self-representationmentioning

confidence: 99%

Simultaneous Subspace Clustering and Cluster Number Estimating Based on Triplet Relationship

Liang

Yang

Cheng

et al. 2019

IEEE Trans. on Image Process.

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In this paper we propose a unified framework to simultaneously discover the number of clusters and group the data points into them using subspace clustering. Real data distributed in a high-dimensional space can be disentangled into a union of low-dimensional subspaces, which can benefit various applications. To explore such intrinsic structure, stateof-the-art subspace clustering approaches often optimize a selfrepresentation problem among all samples, to construct a pairwise affinity graph for spectral clustering. However, a graph with pairwise similarities lacks robustness for segmentation, especially for samples which lie on the intersection of two subspaces. To address this problem, we design a hyper-correlation based data structure termed as the triplet relationship, which reveals high relevance and local compactness among three samples. The triplet relationship can be derived from the self-representation matrix, and be utilized to iteratively assign the data points to clusters. Three samples in each triplet are encouraged to be highly correlated and are considered as a meta-element during clustering, which show more robustness than pairwise relationships when segmenting two densely distributed subspaces. Based on the triplet relationship, we propose a unified optimizing scheme to automatically calculate clustering assignments. Specifically, we optimize a model selection reward and a fusion reward by simultaneously maximizing the similarity of triplets from different clusters while minimizing the correlation of triplets from same cluster. The proposed algorithm also automatically reveals the number of clusters and fuses groups to avoid oversegmentation. Extensive experimental results on both synthetic and real-world datasets validate the effectiveness and robustness of the proposed method.

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“…It relies on the assumption that high-dimensional data points lie in a union of multiple low-dimensional subspaces and aims to group data points into corresponding clusters simultaneously [12]. Owing to its promising performance and good interpretability, a number of clustering algorithms based on subspace clustering have been proposed [31,12,20,36,15,10]. For example, Sparse Subspace Clustering (SSC) [12] obtains a sparsest subspace coefficient matrix for clustering.…”

Section: Introductionmentioning

confidence: 99%

Constrained bilinear factorization multi-view subspace clustering

Zheng

Zhu

Tian

et al. 2020

Knowledge-Based Systems

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A B S T R A C TMulti-view clustering is an important and fundamental problem. Many multi-view subspace clustering methods have been proposed and achieved success in real-world applications, most of which assume that all views share a same coefficient matrix. However, the underlying information of multiview data are not exploited effectively under this assumption, since the coefficient matrices of different views should have the same clustering properties rather than be the same among multiple views. To this end, a novel Constrained Bilinear Factorization Multi-view Subspace Clustering (CBF-MSC) method is proposed in this paper. Specifically, the bilinear factorization with an orthonormality constraint and a low-rank constraint is employed for all coefficient matrices to make all coefficient matrices have the same trace-norm instead of being equivalent, so as to explore the consensus information of multi-view data more effectively. Finally, an algorithm based on the Augmented Lagrangian Multiplier (ALM) scheme with alternating direction minimization is designed to optimize the objective function. Comprehensive experiments tested on six benchmark datasets validate the effectiveness and competitiveness of the proposed approach compared with several state-of-the-art approaches.

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Provable Subspace Clustering: When LRR Meets SSC

Cited by 79 publications

References 41 publications

$\ell_0$ -Motivated Low-Rank Sparse Subspace Clustering

$\ell_0$ -Motivated Low-Rank Sparse Subspace Clustering

Simultaneous Subspace Clustering and Cluster Number Estimating Based on Triplet Relationship

Constrained bilinear factorization multi-view subspace clustering

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