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Deep graph regularized nonnegative Tucker decomposition for image data analysis

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Abstract

Nonnegative Tucker decomposition (NTD) is widely recognized as an effective tool for image analysis. However, the single-layer structure of the original NTD model is insufficient for capturing multiple directional representations and local manifold structural information from the raw image data. To overcome these limitations, we extend the single-layer framework to a deep graph regularized nonnegative Tucker decomposition (DGNTD) structure by harmoniously unifying deep learning and graph regularization terms in NTD. DGNTD constructs a hierarchical deep structure and decomposes image data into several layers that describe the interconnections of different layers throughout the deep structure. Furthermore, DGNTD with graph learning utilizes a graph structure to express the relationships between samples, which allows for the depiction of the inner geometrical relationships between samples while preserving computational feasibility. In addition, tests on three image datasets, including COIL20, ORL, and PIE, are used to assess the effectiveness of the proposed method.

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Data Availability

The open datasets that used in the manuscript have been linked in related parts and the datasets generated during the current study are available from the corresponding author on reasonable request.

Notes

  1. https://www.cs.columbia.edu/CAVE/software/softlib/coil-20.php

  2. https://github.com/saeid436/Face-Recognition-MLP/tree/main/ORL

  3. http://www.ri.cmu.edu/projects/project_418.html

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Acknowledgements

Fatimah Abdul Razak is supported by Universiti Kebangsaan Malaysia under Grant GUP-2021-046. Sakhinah Abu Bakar is supported by Malaysian Ministry of Higher Education under Grant FRGS/1/2020/STG06/UKM/02/6. Qilong Liu is supported by the National Natural Science Foundation of China 12461072 and Guizhou Provincial Basic Research Program (Natural Science) under Grant QKHJC-ZK[2023]YB245. Qingshui Liao is supported by Guizhou Provincial Basic Research Program (Natural Science) under Grant QKHJC-ZK[2023]YB245.

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The idea of this article is proposed by Fatimah Abdul Razak and Sakhinah Abu Bakar, the exact algorithms are provided by Qingshui Liao, the numerical tests are conducted by Qingshui Liao, the English writing is finished by Qingshui Liao and polished by Qilong Liu, Fatimah Abdul Razak and Sakhinah Abu Bakar.

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Correspondence to Fatimah Abdul Razak.

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Liao, Q., Bakar, S.A., Liu, Q. et al. Deep graph regularized nonnegative Tucker decomposition for image data analysis. Appl Intell 55, 76 (2025). https://doi.org/10.1007/s10489-024-05920-1

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