Laplacian Regularized Nonnegative Representation for Clustering and Dimensionality Reduction

Zhao, Yin-Ping; Chen, Long; Chen, C. L. Philip

doi:10.1109/tcsvt.2020.2967424

Cited by 35 publications

(3 citation statements)

References 44 publications

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“…We solve Eq. ( 13) by the alternating direction method of multipliers (ADMM), which is very effective for solving problems with multiple variables and equality constraints [23], [24]. We first introduce an auxiliary matrix D ∈ R n×n , and let D = Z, then Eq.…”

Section: Algorithm For Solving Eq (13)mentioning

confidence: 99%

Semi-Supervised Subspace Clustering via Tensor Low-Rank Representation

Jia

Guanxing

Liu

et al. 2023

IEEE Trans. Circuits Syst. Video Technol.

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Semi-supervised symmetric non-negative matrix factorization (SNMF) utilizes the available supervisory information (usually in the form of pairwise constraints) to improve the clustering ability of SNMF. The previous methods introduce the pairwise constraints from the local perspective, i.e., they either directly refine the similarity matrix element-wisely or restrain the distance of the decomposed vectors in pairs according to the pairwise constraints, which overlook the global perspective, i.e., in the ideal case, the pairwise constraint matrix and the ideal similarity matrix possess the same low-rank structure. To this end, we first propose a novel semi-supervised SNMF model by seeking low-rank representation for the tensor synthesized by the pairwise constraint matrix and a similarity matrix obtained by the product of the embedding matrix and its transpose, which could strengthen those two matrices simultaneously from a global perspective. We then propose an enhanced SNMF model, making the embedding matrix tailored to the above tensor low-rank representation. We finally refine the similarity matrix by the strengthened pairwise constraints. We repeat the above steps to continuously boost the similarity matrix and pairwise constraint matrix, leading to a high-quality embedding matrix. Extensive experiments substantiate the superiority of our method. The code is available at https://github.com/JinaLeejnl/TSNMF.

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Section: Algorithm For Solving Eq (13)mentioning

confidence: 99%

Semi-Supervised Subspace Clustering via Tensor Low-Rank Representation

Jia

Guanxing

Liu

et al. 2023

IEEE Trans. Circuits Syst. Video Technol.

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“…We solve the problem in Eq. ( 4) by alternating direction method of multipliers (ADMM) [18]. By introducing an auxiliary matrix D, we get the equivalent form of Eq.…”

Section: B Optimization Algorithmmentioning

confidence: 99%

Semi-Supervised Subspace Clustering via Tensor Low-Rank Representation

Guanxing¹,

Jia²,

Hou³

2022

Preprint

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In this letter, we propose a novel semi-supervised subspace clustering method, which is able to simultaneously augment the initial supervisory information and construct a discriminative affinity matrix. By representing the limited amount of supervisory information as a pairwise constraint matrix, we observe that the ideal affinity matrix for clustering shares the same low-rank structure as the ideal pairwise constraint matrix. Thus, we stack the two matrices into a 3-D tensor, where a global low-rank constraint is imposed to promote the affinity matrix construction and augment the initial pairwise constraints synchronously. Besides, we use the local geometry structure of input samples to complement the global low-rank prior to achieve better affinity matrix learning. The proposed model is formulated as a Laplacian graph regularized convex low-rank tensor representation problem, which is further solved with an alternative iterative algorithm. In addition, we propose to refine the affinity matrix with the augmented pairwise constraints. Comprehensive experimental results on six commonlyused benchmark datasets demonstrate the superiority of our method over state-of-the-art methods. The code is publicly available at https://github.com/GuanxingLu/Subspace-Clustering.

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“…Xu et al [27] designed a jointly non-negative, sparse and collaborative representation (NSCR) for image recognition. Zhao et al [28] developed a Laplacian regularized non-negative representation (LapNR) method for clustering and dimensionality reduction tasks. Inspired by NRC, Yin et al [29] explored a class-specific residual constraint nonnegative representation (CRNR) for pattern classification.…”

Section: Related Workmentioning

confidence: 99%

Affine Non-negative Collaborative Representation Based Pattern Classification

Yin,

Wu,

Feng

et al. 2020

Preprint

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During the past decade, representation-based classification methods have received considerable attention in pattern recognition. In particular, the recently proposed non-negative representation based classification (NRC) method has been reported to achieve promising results in a wide range of classification tasks. However, NRC has two major drawbacks. First, there is no regularization term in the formulation of NRC, which may result in unstable solution and misclassification. Second, NRC ignores the fact that data usually lies in a union of multiple affine subspaces, rather than linear subspaces in practical applications. To address the above issues, this paper presents an affine non-negative collaborative representation (ANCR) model for pattern classification. To be more specific, ANCR imposes a regularization term on the coding vector. Moreover, ANCR introduces an affine constraint to better represent the data from affine subspaces. The experimental results on several benchmarking datasets demonstrate the merits of the proposed ANCR method. The source code of our ANCR is publicly available at https://github.com/yinhefeng/ANCR.

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Laplacian Regularized Nonnegative Representation for Clustering and Dimensionality Reduction

Cited by 35 publications

References 44 publications

Semi-Supervised Subspace Clustering via Tensor Low-Rank Representation

Semi-Supervised Subspace Clustering via Tensor Low-Rank Representation

Semi-Supervised Subspace Clustering via Tensor Low-Rank Representation

Affine Non-negative Collaborative Representation Based Pattern Classification

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