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Volume 34 Issue 2
March  2019
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Xiang-Chu Feng, Chen-Ping Zhao, Si-Long Peng, Xi-Yuan Hu, Zhao-Wei Ouyang. Plug-and-Play Based Optimization Algorithm for New Crime Density Estimation[J]. Journal of Computer Science and Technology, 2019, 34(2): 476-493. DOI: 10.1007/s11390-019-1920-1
Citation: Xiang-Chu Feng, Chen-Ping Zhao, Si-Long Peng, Xi-Yuan Hu, Zhao-Wei Ouyang. Plug-and-Play Based Optimization Algorithm for New Crime Density Estimation[J]. Journal of Computer Science and Technology, 2019, 34(2): 476-493. DOI: 10.1007/s11390-019-1920-1
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Plug-and-Play Based Optimization Algorithm for New Crime Density Estimation

  • 1 School of Mathematics and Statistics, Xidian University, Xi'an 710126, China;
    2 School of Mathematical Science, Henan Institute of Science and Technology, Xinxiang 453003, China;
    3 Institute of Automation, Chinese Academy of Sciences, Beijing 100190, China;
    4 School of Computer and Control Engineering, University of Chinese Academy of Sciences, Beijing 100190, China;
    5 Research Center of Beijing Visystem Co. Ltd., Beijing 100190, China

Funds: This work was partially supported by the National Natural Science Foundation of China under Grant Nos. 61772389 and 61871260, the Open Project of National Engineering Laboratory for Forensic Science of China under Grant No. 2017NELKFKT02, and the Key Scientific Research Projects in Henan Colleges and Universities of China under Grant No. 19A110015.
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  • Author Bio:

    Xiang-Chu Feng received his B.S. degree in computational mathematics from Xi'an Jiaotong University, Xi'an, in 1984, and his M.S. and Ph.D. degrees in applied mathematics from Xidian University, Xi'an, in 1989 and 1999, respectively. He is currently a professor in the School of Mathematics and Statistics, Xidian University, Xi'an. His research interests include numerical analysis, wavelets, and partial differential equations for image processing.

  • Corresponding author:

    Chen-Ping Zhao E-mail: zcp0378@163.com

  • Received Date: July 29, 2017
  • Revised Date: January 16, 2019
  • Published Date: March 04, 2019
    Abstract
  • Different from a general density estimation, the crime density estimation usually has one important factor: the geographical constraint. In this paper, a new crime density estimation model is formulated, in which the regions where crime is impossible to happen, such as mountains and lakes, are excluded. To further optimize the estimation method, a learning-based algorithm, named Plug-and-Play, is implanted into the augmented Lagrangian scheme, which involves an off-the-shelf filtering operator. Different selections of the filtering operator make the algorithm correspond to several classical estimation models. Therefore, the proposed Plug-and-Play optimization based estimation algorithm can be regarded as the extended version and general form of several classical methods. In the experiment part, synthetic examples with different invalid regions and samples of various distributions are first tested. Then under complex geographic constraints, we apply the proposed method with a real crime dataset to recover the density estimation. The state-of-the-art results show the feasibility of the proposed model.
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    • References (29)
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    1. Yingjun Wang, Chenping Zhao, Hongwei Jiao, et al. Lp-Method-Noise Based Regularization Model for Image Restoration. IEEE Access, 2020, 8: 146039. DOI:10.1109/ACCESS.2020.3015140

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