Graph regularized discriminative nonnegative tucker decomposition for tensor data representation

Jing, Wenjing; Lu, Linzhang; Liu, Qilong

doi:10.1007/s10489-023-04738-7

Cited by 3 publications

(3 citation statements)

References 35 publications

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“…To evaluate the effectiveness of the proposed AOGNTD methods, we compare the clustering performance of our methods with the other six state-of-the-art and previously mentioned methods that are k-means [38], NMF [11,12], GNMF [38], GDNMF [39], NTD [15] and GNTD [20,21]. In order to distinguish DNMF of the original article from DNMF with the label information [27], we have written DNMF [39,40] as GDNMF in Table 3.…”

Section: Compared Methodsmentioning

confidence: 99%

“…Recent efforts have extended NTD to boost calculation efficiency and meet different demands in actual applications by incorporating suitable constrain conditions with NTD, including smoothness [16,17], graph Laplacian [18][19][20][21][22][23][24], sparsity [25], supervision [26][27][28], just to name a few. For examples, Liu et al stated a graph regularized L p smooth NTD method by adding the graph regularization and L p smooth constraint into NTD to retain smooth and more accurate solution of the objective function [17].…”

Section: Introductionmentioning

confidence: 99%

“…Jing et al recommended a label constrained NTD, using partial labels to construct label matrix. Then they embed the label term and graph regularization term into NTD for guiding the algorithm to obtain more correct categories in clustering tasks [27]. To make use of the available label information of sample data, Qiu et al built up a semi-supervised NTD (SNTD) model by propagating the limited label information and learning the non-negative tensor representation [28].…”

Section: Introductionmentioning

confidence: 99%

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Approximately orthogonal non-negative Tucker decomposition with graph regularized for multiway dimensionality reduction

Gao,

Lu,

Liu

2024

Preprint

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Non-negative Tucker decomposition (NTD) is one of the renowned technique in feature extraction and representation for non-negative high-dimensional tensor data. The main focus behind NTD is how to factorize the data to get hold of a high quality data representation from multidimensional directions. However, NTD does not conserve the geometrical structure of the data space and does not consider relationship and property among columns of the factor matrices. In this paper, by using approximately orthogonal constraint and graph regularized constraint , we manage to capture nonlinear local features of data space and further enhance expressiveness of the NTD clustering method. First, based on the uni-side and bi-side approximate orthogonality, we propose two novel approximately orthogonal non-negative Tucker decomposition with graph regularized models, which not only in part make factor matrix tend to be orthogonality, but also preserve the geometrical information from high-dimensional tensor data. Then we develop the iterative updating algorithm depended on multiplicative update rule to solve the proposed models, and provide its convergence and computational complexity. Finally, we use numerical experimental results to demonstrate the effectiveness, robustness and efficiency of the proposed new methods on the real-world image datasets.

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Section: Compared Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Approximately orthogonal non-negative Tucker decomposition with graph regularized for multiway dimensionality reduction

Gao,

Lu,

Liu

2024

Preprint

Self Cite

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Semi-supervised regression via embedding space mapping and pseudo-label smearing

Liu,

Zhang,

Qian

et al. 2024

Appl Intell

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Non-negative Tucker decomposition with double constraints for multiway dimensionality reduction

Gao,

Lu,

Liu

2024

MATH

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<p>Nonnegative Tucker decomposition (NTD) is one of the renowned techniques in feature extraction and representation for nonnegative high-dimensional tensor data. The main focus behind the NTD-like model was how to factorize the data to get ahold of a high quality data representation from multidimensional directions. However, existing NTD-like models do not consider relationship and properties between the factor matrix of columns while preserving the geometric structure of the data space. In this paper, we managed to capture nonlinear local features of data space and further enhance expressiveness of the NTD clustering method by syncretizing organically approximately orthogonal constraint and graph regularized constraint. First, based on the uni-side and bi-side approximate orthogonality, we flexibly proposed two novel approximately orthogonal NTD with graph regularized models, which not only in part make the factor matrix tend to be orthogonality, but also preserve the geometrical information from high-dimensional tensor data. Second, we developed the iterative updating algorithm dependent on the multiplicative update rule to solve the proposed models, and provided its convergence and computational complexity. Finally, we used numerical experimental results to demonstrate the effectiveness, robustness, and efficiency of the proposed new methods on the real-world image datasets.</p>

show abstract

Graph regularized discriminative nonnegative tucker decomposition for tensor data representation

Cited by 3 publications

References 35 publications

Approximately orthogonal non-negative Tucker decomposition with graph regularized for multiway dimensionality reduction

Approximately orthogonal non-negative Tucker decomposition with graph regularized for multiway dimensionality reduction

Semi-supervised regression via embedding space mapping and pseudo-label smearing

Non-negative Tucker decomposition with double constraints for multiway dimensionality reduction

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