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Double truncated nuclear norm-based matrix decomposition with application to background modeling

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Abstract

Many topics in pattern recognition and machine learning, such as subspace learning, image restoration, background modeling, can be viewed as the matrix decomposing problem. Double nuclear norm-based matrix decomposition (DNMD) is a new emerging method for dealing with the image data corrupted by continuous occlusion. The method uses a unified low rank assumption to characterize the real image data and continuous occlusion. However, one major limitation of the nuclear norm is that each singular value is treated equally, since the nuclear norm is defined as the sum of all singular values. Thus the rank function may not be well approximated in practice. To overcome this drawback, this paper presents double truncated nuclear norm-based matrix decomposition (DTNMD). The truncated nuclear norm can reflect the rank function more accurate and robust. Experimental results show encouraging results of the proposed algorithm in comparison to the state-of-the-art matrix completion methods on both synthetic and real visual datasets.

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Notes

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

  2. http://perception.csl.illinois.edu/matrix-rank/sample_code.html.

  3. http://www.escience.cn/people/fpnie/index.html.

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Acknowledgements

This research is supported in part by the National Key R&D Program under Grant 2017YFC0804002, the National Science Foundation of China under Grant Nos. U1831127, 61603192, 61572257, 61772277 and 61772254, the 2011 Collaborative Innovation Center of Internet of Things Technology and Intelligent Systems under Grant Nos. IIC1705, the Jiangsu Key Laboratory of Image and Video Understanding for Social Safety (Nanjing University of Science and Technology) (Grant No. 30916014107), the China Postdoctoral Science Foundation funded project (Grant No. 2017M611656).

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  1. Zhangjing Yang and Hui Zhang contributed equally to this work.

Authors and Affiliations

  1. School of Technology, Nanjing Audit University, Nanjing, 211815, China

    Zhangjing Yang, Hui Zhang, Fanlong Zhang & Guowei Yang

  2. School of Computer and Software, Nanjing University of Information Science & Technology, Nanjing, 210044, China

    Danhua Xu

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  1. Zhangjing Yang
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  2. Hui Zhang
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  3. Danhua Xu
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  4. Fanlong Zhang
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  5. Guowei Yang
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Correspondence to Fanlong Zhang.

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Yang, Z., Zhang, H., Xu, D. et al. Double truncated nuclear norm-based matrix decomposition with application to background modeling. J Ambient Intell Human Comput 14, 14921–14930 (2023). https://doi.org/10.1007/s12652-018-1148-x

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