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Graph regularized discriminative nonnegative tucker decomposition for tensor data representation

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Abstract

Tensor factorization has been widely applied in computer vision and machine learning area. Nonnegative Tucker decomposition (NTD) is a popular tensor factorization technique. However, it neglects the geometrical structure of the data space and the available label information of sample data, lowering the data representation performance. To overcome this defect, in this paper, we propose a novel semi-supervised NTD method, named graph regularized discriminative nonnegative Tucker decomposition (GDNTD), which incorporates the graph construction of the data space and the available label information of the sample data into NTD. Specifically, a graph construction is utilized to preserve the geometric structure between data by a graph regularization term. Then, a label matrix is presented for guiding the data representation by a label constraint regularization term. Finally, based on the NTD property of maintaining the internal structure of data, the graph regularizer and the label regularizer are integrated into NTD to generate the proposed method. Thus, GDNTD can extract the part-based representation, preserve the local geometrical structure of the data space, and improve the discriminative ability of the learned model simultaneously, greatly boosting the model’s data representation performance. We test the proposed method through a set of evaluations on four image datasets. Experimental results show that the GDNTD method outperforms state-of-the-art approaches, demonstrating its strong potential for data representation.

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Notes

  1. http://www.cad.zju.edu.cn/home/dengcai/Data/MLData.html

  2. http://www.cad.zju.edu.cn/home/dengcai/Data/FaceData.html

  3. https://cs.nyu.edu/~roweis/data.html

  4. http://www.cad.zju.edu.cn/home/dengcai/Data/MLData.html

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Acknowledgements

Linzhang Lu is supported by the National Natural Science Foundation of China under Grant 12161020, 12061025. Qilong Liu is supported by Natural Science Foundation of Educational Commission of Guizhou Province under Grant Qian-Jiao-He KY Zi [2021]298 and Guizhou Provincial Basis Research Program (Natural Science) (QKHJC-ZK[2023]YB245).

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Authors and Affiliations

  1. School of Mathematical Sciences, Guizhou Normal University, Guiyang, People’s Republic of China

    Wenjing Jing, Linzhang Lu & Qilong Liu

  2. School of Mathematical Sciences, Xiamen University, Xiamen, People’s Republic of China

    Linzhang Lu

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  1. Wenjing Jing
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Correspondence to Linzhang Lu.

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Wenjing Jing, Linzhang Lu and Qilong Liu contributed equally to this work.

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Jing, W., Lu, L. & Liu, Q. Graph regularized discriminative nonnegative tucker decomposition for tensor data representation. Appl Intell 53, 23864–23882 (2023). https://doi.org/10.1007/s10489-023-04738-7

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