Manifold Regularization Nonnegative Triple Decomposition of Tensor Sets for Image Compression and Representation

Wu, Fengsheng; Li, Chaoqian; Li, Yaotang

doi:10.1007/s10957-022-02001-6

Cited by 3 publications

(5 citation statements)

References 12 publications

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“…Now, we are going to show that the update rule for A (1) shown in ( 12) is exactly the same as that shown in (20) with a proper auxiliary function. Considering the ith row and jth column entry [A (1) ] ij in A (1) , we use F ij to denote the part of the objective function (7) that is relevant only to [A (1) ] ij .…”

Section: Convergence Analysismentioning

confidence: 93%

“…We are going to state that the update for W expressed as ( 17) is equal to the update (20) with an appropriate auxiliary function. Considering the ith row and jth column entry W ij in W, we use Fij to denote the part of the objective function (7) that is only relevant to W ij .…”

Section: Convergence Analysismentioning

confidence: 99%

“…Qiu et al [19] proposed a graph regularized nonnegaitve Tucker decomposition (GNTD) method by applying Laplacian regularization to the last nonnegative factor matrix. Subsequently, Wu et al [20] proposed a manifold regularization nonnegative triple decomposition (MRNTriD) of tensor sets that takes advantage of tensor geometry information. These graph-based manifold learning methods perform well in clustering.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Hypergraph regularized nonnegative triple decomposition for multiway data analysis

Liao,

Liu,

Razak

2024

Preprint

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Tucker decomposition is widely used for image representation, data reconstruction , and machine learning tasks, but the calculation cost for updating the Tucker core is high. Bilevel form of triple decomposition (TriD) overcomes this issue by decomposing the Tucker core into three low-dimensional third-order factor tensors and plays an important role in the dimension reduction of data representation. TriD, on the other hand, is incapable of precisely encoding similarity relationships for tensor data with a complex manifold structure. To address this shortcoming, we take advantage of hypergraph learning and propose a novel hypergraph regu-larized nonnegative triple decomposition for multiway data analysis that employs the hypergraph to model the complex relationships among the raw data. Furthermore , we develop a multiplicative update algorithm to solve our optimization problem and theoretically prove its convergence. Finally, we perform extensive numerical tests on six real-world datasets, and the results show that our proposed algorithm outperforms some state-of-the-art methods.

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Section: Convergence Analysismentioning

confidence: 93%

Section: Convergence Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Hypergraph regularized nonnegative triple decomposition for multiway data analysis

Liao,

Liu,

Razak

2024

Preprint

View full text Add to dashboard Cite

show abstract

“…Liu et al 27 presented a technique known as graph regularized smooth NTD (GSNTD) via embedding graph regularization and smooth constraint into the original model of NTD. Subsequently, Wu et al 28 proposed a manifold regularization nonnegative triple decomposition (MRNTriD) of tensor sets that takes advantage of tensor geometry information. These graph-based manifold learning methods perform well in clustering.…”

Section: Introductionmentioning

confidence: 99%

Hypergraph regularized nonnegative triple decomposition for multiway data analysis

Liao,

Liu,

Razak

2024

Sci Rep

View full text Add to dashboard Cite

Tucker decomposition is widely used for image representation, data reconstruction, and machine learning tasks, but the calculation cost for updating the Tucker core is high. Bilevel form of triple decomposition (TriD) overcomes this issue by decomposing the Tucker core into three low-dimensional third-order factor tensors and plays an important role in the dimension reduction of data representation. TriD, on the other hand, is incapable of precisely encoding similarity relationships for tensor data with a complex manifold structure. To address this shortcoming, we take advantage of hypergraph learning and propose a novel hypergraph regularized nonnegative triple decomposition for multiway data analysis that employs the hypergraph to model the complex relationships among the raw data. Furthermore, we develop a multiplicative update algorithm to solve our optimization problem and theoretically prove its convergence. Finally, we perform extensive numerical tests on six real-world datasets, and the results show that our proposed algorithm outperforms some state-of-the-art methods.

show abstract

“…Specifically, a tensor is a generalization of a vector or matrix to higher dimensions [5, 10-12, 34, 35, 40]. Tensors have applications in diverse areas such as machine learning, signal processing, biology, applied mechanics, data mining, pattern recognition, and numerical approaches algorithms for computing some generalized tensor and matrix equations [1,18,22,24,25,28,31,33,37,[51][52][53][54][55]. Hamilton [19] was first presented the quaternion algebra over the real field R…”

Section: Introductionmentioning

confidence: 99%

Algebraic conditions and general solution to a system of quaternion tensor equations with applications

Mehany¹,

Wang²

2022

Preprint

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This paper investigates the necessary and sufficient algebraic conditions to a constrained system of Sylvester-type quaternion tensor equations. An explicit formula of the general solution regarding the Moore-Penrose inverses of some block given tensors is obtained. As an application of a particular case, we establish the solvability conditions and the general solution to a system of Sylvester-type quaternion tensor equations involving η-Hermitian unknowns. An algorithm with a numerical example is proposed to compute the general solution of the main system.

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Manifold Regularization Nonnegative Triple Decomposition of Tensor Sets for Image Compression and Representation

Cited by 3 publications

References 12 publications

Hypergraph regularized nonnegative triple decomposition for multiway data analysis

Hypergraph regularized nonnegative triple decomposition for multiway data analysis

Hypergraph regularized nonnegative triple decomposition for multiway data analysis

Algebraic conditions and general solution to a system of quaternion tensor equations with applications

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