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

Gao, Quanxue; Xia, Wei; Wan, Zhizhen; Xie, Deyan; Zhang, Pu

doi:10.1609/aaai.v34i04.5807

Cited by 141 publications

(37 citation statements)

References 14 publications

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“…As shown, the proposed TLD model also outperforms all the other compared methods by a large margin. Compared with GLMSC method [30], our results improve the NMI metric from 0.932 to 0.974, and improve the ACC metric from 0.904 to 0.987. Table 7 shows the comparison results on the MITIndoor-67 dataset.…”

Section: B Performance Of the Proposed Modelmentioning

confidence: 86%

“…We compare the proposed method with eight representative clustering algorithms include two single-view clustering methods (i.e., SPC best [59] and LRR best [11]) and six multiview clustering methods (i.e., RMSC [20], DiMSC [39], LTMSC [19], t-SVD-MSC [22], ETLMSC [31], GLMSC [30]).…”

Section: ) Compared Methodsmentioning

confidence: 99%

“…By constructing a tensor based on multi-view transition probability matrices of the Markov chain, Wu et al [31] proposed a novel essential tensor learning method to explore the high order correlations for multi-view representation. To improve the robustness and clustering performance, Gao et al [30] studied the weighted tensor-nuclear norm based on t-SVD and its application to multi-view subspace clustering by exploiting the high order correlations embedded in different views.…”

Section: Related Workmentioning

confidence: 99%

“…The clustering results of our method and the other eight state-of-the-art methods on the Yale dataset, Extended YaleB dataset, ORL dataset, Notting-Hill dataset, Scene-15 dataset, MITIndoor-67 dataset and COIL-20 dataset are shown in Table 2 -Table 8, respectively. For fair comparisons, we use the best results of competitors which are reported in [19], [22], [30], [31]. For some datasets, the original paper doesn't show the results, and we denote "-" in the tables for this case.…”

Section: B Performance Of the Proposed Modelmentioning

confidence: 99%

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Robust Multiview Subspace Clustering of Images via Tighter Rank Approximation

et al. 2021

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In this paper, we focus on the multi-view subspace clustering problem under the framework of third order tensor. Recently, tensor nuclear norm (TNN) has been widely used in the multi-view subspace clustering problem. It is known that TNN is a convex surrogate of the tensor rank. However, TNN is linearly proportional to the sum of the singular values. Thus solving the TNN minimization problem will overpenalize the large singular values and lead to a sub-optimal solution. To address this issue, in this paper, a novel tighter tensor log-determinant (TLD) regularizer is proposed to better approximate the tensor rank. Although the proposed method is non-convex, a closed-form solution has been deduced via solving the Euler-Lagrange equation. A corresponding algorithm associated with augmented Lagrangian multipliers is established and the constructed convergent sequence to the Karush-Kuhn-Tucker (KKT) critical point solution is mathematically validated in detail. Extensive experiments indicate that the proposed model achieves significant improvements compared to the state-of-the-art convex subspace clustering models.

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Section: B Performance Of the Proposed Modelmentioning

confidence: 86%

Section: ) Compared Methodsmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: B Performance Of the Proposed Modelmentioning

confidence: 99%

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Robust Multiview Subspace Clustering of Images via Tighter Rank Approximation

et al. 2021

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“…Multiview clustering has become an active topic in pattern analysis and artificial intelligence due to the ubiquitous multiview data in real applications [5], [11], [21], [23], [27], [35]. Being the efficiency of learning affinity matrix, which well characterizes the relationship in data, MVSC has become one of the most representative clustering techniques.…”

Section: Multiview Subspace Clusteringmentioning

confidence: 99%

Multiview Subspace Clustering by an Enhanced Tensor Nuclear Norm

Xia

Zhang

Gao

et al. 2022

IEEE Trans. Cybern.

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Despite the promising preliminary results, tensorsingular value decomposition (t-SVD)-based multiview subspace is incapable of dealing with real problems, such as noise and illumination changes. The major reason is that tensor-nuclear norm minimization (TNNM) used in t-SVD regularizes each singular value equally, which does not make sense in matrix completion and coefficient matrix learning. In this case, the singular values represent different perspectives and should be treated differently. To well exploit the significant difference between singular values, we study the weighted tensor Schatten p-norm based on t-SVD and develop an efficient algorithm to solve the weighted tensor Schatten p-norm minimization (WTSNM) problem. After that, applying WTSNM to learn the coefficient matrix in multiview subspace clustering, we present a novel multiview clustering method by integrating coefficient matrix learning and spectral clustering into a unified framework. The learned coefficient matrix well exploits both the cluster structure and high-order information embedded in multiview views. The extensive experiments indicate the efficiency of our method in six metrics.Index Terms-Multiview clustering, spectral clustering, tensorsingular value decomposition (t-SVD), weighted nuclear norm. I. INTRODUCTIONM ULTIVIEW data are ubiquitous in machine learning and artificial intelligence, and help provide complementary information embedded in multiviews for multiview clustering. Multiview clustering aims to separate multiview data into several meaningful groups and has become Manuscript

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