Journal of Computer Science and Technology

, Volume 34, Issue 2, pp 476–493 | Cite as

Plug-and-Play Based Optimization Algorithm for New Crime Density Estimation

  • Xiang-Chu Feng
  • Chen-Ping ZhaoEmail author
  • Si-Long Peng
  • Xi-Yuan Hu
  • Zhao-Wei Ouyang
Regular Paper


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.


crime density estimation augmented Lagrangian strategy Plug-and-Play filtering operator 


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We would like to thank the anonymous reviewers for their careful work and thoughtful suggestions that have helped improve this paper substantially, and thank Dr. Shi-Jun Wang of Research Center of Beijing Visystem Co. Ltd. for the fruitful discussion.

Supplementary material

11390_2019_1920_MOESM1_ESM.pdf (473 kb)
ESM 1 (PDF 473 kb)


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Copyright information

© Springer Science+Business Media, LLC & Science Press, China 2019

Authors and Affiliations

  • Xiang-Chu Feng
    • 1
  • Chen-Ping Zhao
    • 1
    • 2
    Email author
  • Si-Long Peng
    • 3
    • 4
  • Xi-Yuan Hu
    • 3
    • 4
    • 5
  • Zhao-Wei Ouyang
    • 1
  1. 1.School of Mathematics and StatisticsXidian UniversityXi’anChina
  2. 2.School of Mathematical ScienceHenan Institute of Science and TechnologyXinxiangChina
  3. 3.Institute of AutomationChinese Academy of SciencesBeijingChina
  4. 4.School of Computer and Control EngineeringUniversity of Chinese Academy of SciencesBeijingChina
  5. 5.Research Center of Beijing Visystem Co. Ltd.BeijingChina

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