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

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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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Acknowledgements

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.

Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, Xidian University, Xi’an, 710126, China

    Xiang-Chu Feng, Chen-Ping Zhao & Zhao-Wei Ouyang

  2. School of Mathematical Science, Henan Institute of Science and Technology, Xinxiang, 453003, China

    Chen-Ping Zhao

  3. Institute of Automation, Chinese Academy of Sciences, Beijing, 100190, China

    Si-Long Peng & Xi-Yuan Hu

  4. School of Computer and Control Engineering, University of Chinese Academy of Sciences, Beijing, 100190, China

    Si-Long Peng & Xi-Yuan Hu

  5. Research Center of Beijing Visystem Co. Ltd., Beijing, 100190, China

    Xi-Yuan Hu

Authors
  1. Xiang-Chu Feng
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  2. Chen-Ping Zhao
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  3. Si-Long Peng
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  4. Xi-Yuan Hu
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  5. Zhao-Wei Ouyang
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Correspondence to Chen-Ping Zhao.

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Feng, XC., Zhao, CP., Peng, SL. et al. Plug-and-Play Based Optimization Algorithm for New Crime Density Estimation. J. Comput. Sci. Technol. 34, 476–493 (2019). https://doi.org/10.1007/s11390-019-1920-1

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  • DOI: https://doi.org/10.1007/s11390-019-1920-1

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