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Discriminative low-rank representation with Schatten-p norm for image recognition

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Abstract

Low-rank representation (LRR) has attracted much attention recently due to its efficacy in a rich variety of real world applications. Recently, the non-convex regularization has become widely used in the rank minimization problem. In this paper, we propose a discriminative low-rank representation with Schatten-p norm (DLRR-SPN) to learn a robust and discriminative affinity matrix for image recognition. To this end, we first impose the Schatten-p norm regularization on the representation matrix to learn the global structure of data. Moreover, the adaptive distance penalty is used to preserve the local neighbor relationship of data. The objective function is formulated as a Schatten-p norm minimization problem, which can be solved via alternating direction method of multipliers (ADMM). To enhance the separation ability of the discriminative affinity matrix for semi-supervised recognition problem, the angular information of the principal directions of the low-rank representation is further exploited. Finally, an effective semi-supervised classifier is utilized on the learned affinity matrix for final prediction. Extensive experimental results on image recognition demonstrate the effectiveness of the proposed method and its superiority in performance over the related state-of-the-art methods.

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Notes

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

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

  3. http://www2.ece.ohio-state.edu/~aleix/ARdatabase.html

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

  5. http://cs.nyu.edu/~roweis/data.html

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Acknowledgements

This work was supported by the National Basic Research Program of China (973 Program) under Grant no. 2013CB329404, the National Natural Science Foundation of China under Grant no. 61572393, the Basic Science Research of Shaanxi province under Grant 2018JQ1038, and the Special Fund for Basic Scientific Research of Central Colleagues, Chang’an University no. 310812171006.

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Authors and Affiliations

  1. School of Science, Chang’an University, Xi’an, China

    Changpeng Wang

  2. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, China

    Jiangshe Zhang & Guang Shi

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  1. Changpeng Wang
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  2. Jiangshe Zhang
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  3. Guang Shi
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Correspondence to Changpeng Wang.

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Wang, C., Zhang, J. & Shi, G. Discriminative low-rank representation with Schatten-p norm for image recognition. Multimed Tools Appl 78, 23075–23095 (2019). https://doi.org/10.1007/s11042-019-7653-x

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  • DOI: https://doi.org/10.1007/s11042-019-7653-x

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