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Chinese Annals of Mathematics, Series B

, Volume 40, Issue 6, pp 949–966 | Cite as

Deep Learning for Real-Time Crime Forecasting and Its Ternarization

  • Bao WangEmail author
  • Penghang Yin
  • Andrea Louise Bertozzi
  • P. Jeffrey BrantinghamEmail author
  • Stanley Joel Osher
  • Jack XinEmail author
Article
  • 12 Downloads

Abstract

Real-time crime forecasting is important. However, accurate prediction of when and where the next crime will happen is difficult. No known physical model provides a reasonable approximation to such a complex system. Historical crime data are sparse in both space and time and the signal of interests is weak. In this work, the authors first present a proper representation of crime data. The authors then adapt the spatial temporal residual network on the well represented data to predict the distribution of crime in Los Angeles at the scale of hours in neighborhood-sized parcels. These experiments as well as comparisons with several existing approaches to prediction demonstrate the superiority of the proposed model in terms of accuracy. Finally, the authors present a ternarization technique to address the resource consumption issue for its deployment in real world. This work is an extension of our short conference proceeding paper [Wang, B., Zhang, D., Zhang, D. H., et al., Deep learning for real time Crime forecasting, 2017, arXiv: 1707.03340].

Keywords

Crime representation Spatial-temporal deep learning Real-time forecasting Ternarization 

2000 MR Subject Classification

00A69 65C50 

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Notes

Acknowledgments

The authors thank the Los Angeles Police Department for providing the crime data for this paper.

References

  1. [1]
    Chen, P., Yuan, H. and Shu, X., Forecasting crime using the arima model, Proceeding of the 5th IEEE International Conference on Fuzzy Systems and Knowledge Discovery, 5, 2008, 627–630.Google Scholar
  2. [2]
    Chen, X., Cho, Y. and Jang, S., Crime prediction using twitter sentiment and weather, Systems and Information Engineering Design Symposium, 2015, 63–68, DOI:10.1109/SIEDS.2015.7117012.Google Scholar
  3. [3]
    Chetlur, S., Woolley, C. Vandermersch, P., et al., cuDNN: Efficient primitives for deep learning, 2014, arXiv:1410.0759.Google Scholar
  4. [4]
    Choillet, F., Keras: Keep learning for humans, 2015, https://doi.org/github.com/fchollet/keras.Google Scholar
  5. [5]
    Courbariaux, M., Bengio, Y. and David, J., Binaryconnect: Training deep neural networks with binary weights during propagations, Advances in Neural Information Processing Systems, 28, 2015, 3123C3131.Google Scholar
  6. [6]
    Courbariaux, M., Hubara, I., Soudry, D., et al., Binarized neural networks: Training neural networks with weights and activations constrained to +1 or -1, CoRR, 2016, arXiv: 1602.02830.Google Scholar
  7. [7]
    Dieleman, S., Schlter, J., Raffel. C., et al., Lasagne: First release., 2015, https://doi.org/lasagne.readthedocs.io/en/latest/.Google Scholar
  8. [8]
    Gerber, M., Predicting crime using twitter and kernel density estimation, Decision Support System, 61, 2014, 115–125.CrossRefGoogle Scholar
  9. [9]
    He, K. M., Zhang, X. Y., Ren, S. Q. and Sun, J., Deep residual learning for image recognition, CVPR, 2016, 770–778.Google Scholar
  10. [10]
    Hochreiter, S. and Schmidhuber, J., Long short-term memory, Neural Comput, 9, 1997, 1735–1780.CrossRefGoogle Scholar
  11. [11]
    Holden, D., Komura, T. and Saito, J., Phase-functioned neural networks for character control, ACM Transactions on Graphics, 36, 2017, 13 pages.CrossRefGoogle Scholar
  12. [12]
    Ioffe, S. and Szegedy, C., Batch normalization: Accelerating deep network training by reducing internal covariate shift, 2015, arXiv:1502.03167.Google Scholar
  13. [13]
    Jain, A., Zamir, A. R., Savarese, S. and Saxena, A., Structural-rnn: Deep learning on spatio-temporal graphs, CVPR, 2016, arXiv:1511.05298.Google Scholar
  14. [14]
    Kang, H. W. and Kang, H.-B., Prediction of crime occurrence from multi-modal data using deep learning, Phos ONE., 12, 2017, DOI:10.1371/journal.pone.0176244.MathSciNetCrossRefGoogle Scholar
  15. [15]
    Kingma, D. P. and Ba, J., Adam: A method for stochastic optimization, ICLR, 2015, arXiv:1412,6980.Google Scholar
  16. [16]
    LeCun, Y., Bengion, Y. and Hinton, C., Deep learning, Nature, 521, 2015, 436–444.CrossRefGoogle Scholar
  17. [17]
    Li, F., Zhang, B. and Liu, B., Ternary weight networks, NIPS Workshop, 2016, https://doi.org/arxiv.org/abs/1605.04711.Google Scholar
  18. [18]
    Li, H., De, S., Xu, Z., et al., Training quantized nets: A deeper understanding, 2017, arXiv:1706.02379.Google Scholar
  19. [19]
    Li, Y., Zemel, R., Brockschmidt, M. and Tarlow, D., Gated graph sequence neural network, ICLR, 2016, https://doi.org/arxiv.org/abs/1511.05493.Google Scholar
  20. [20]
    Mohler, G. O., Short, M. B., Brantingham, P. J., et al., Self-exciting point process modeling of crime, J. Amer. Statist. Assoc, 106(493), 2011, 100–108.MathSciNetCrossRefGoogle Scholar
  21. [21]
    Mohler, G. O., Short, M. B. and Brantingham, P. J., The concentration dynamics tradeoff in crime hot spotting, Unraveling the Crime-Place Connection: New Directions in Theory and Policy., 22, 2017, 21 pages.Google Scholar
  22. [22]
    Osher, S., Wang, B., Yin, P., et al., Laplacian smoothing gradient descent, 2018, arXiv:1806.06317.Google Scholar
  23. [23]
    Rastegari, M., Ordonez, V., Redmon, J. and Farhadi, A., Xnor-net: Imagenet classification using binary convolutional neural networks, EGGV, 2016, arXiv:1603.05279.Google Scholar
  24. [24]
    Short, M. B., Mohler, G. O., Brantingham, P. J. and Tita, G. E., Gang rivalry dynamics via coupled point process network, Discrete Contin. Dyn. Syst. Ser. B, 19(5), 2014, 1459–1477.MathSciNetCrossRefGoogle Scholar
  25. [25]
    Short, M. B., Bertozzi, A. L. and Brantingham, P. J., Nonlinear patterns in urban crime: Hotspots, bifurcations, and suppression, SIAM J. Appl. Dyn. Syst., 9(2), 2010, 462–483.MathSciNetCrossRefGoogle Scholar
  26. [26]
    Short, M. B., Brantingham, P. J., Bertozzi, A. L. and Tita, G. E., Dissipation and displacement of hotspots in reaction-diffusion models of crime, Proc. Nat. Acad. Sci, 107(9), 2010, 3961–3965.CrossRefGoogle Scholar
  27. [27]
    Short, M. B., D'Orsogna, M. R., Pasour, V. B., et al., Persistent heat signature for pose-oblivious matching of incomplete models, M3AS: Mathematical Models and Methods in Applied Sciences, 18, 2008, 1249–1267.Google Scholar
  28. [28]
    Stomakhin, A., Short, M. B. and Bertozzi, A. L., Reconstruction of missing data in social networks based on temporal patterns of interactions, Inverse Problems, 27(11), 2011, 15 pages.Google Scholar
  29. [29]
    The Theano Development Team, Theano: A python framework for fas computation of mathematical expressions, 2015, arXiv: 1605.02688.Google Scholar
  30. [30]
    Wang, B., Zhang, D., Zhang, D. H., et al., Deep Learning for Real Time Crime Forecasting, 2017, arXiv: 1707.03340.Google Scholar
  31. [31]
    Wang, X., Gerber, M. S. and Brown, D. E., Automatic crime prediction using events extracted from twitter posts, International Conference on Social Computing, Behavioral-Cultural Modeling, and Prediction, 2012, 231–238, DOI:10.1007/978-3-642-29047-328.CrossRefGoogle Scholar
  32. [32]
    Yin, P., Zhang, S., Xin, J. and Qi, Y., Quantization and Training of Low Bit-Width Convolutional Neural Networks for Object Detection, 2016, arXiv:1612.06052.Google Scholar
  33. [33]
    Zhang, J. B., Zheng, Y. and Qi, D. R., Deep spatio-temporal residual networks for citywide crowd flows prediction, AAAI, 2017, arXiv:1610.00081.Google Scholar
  34. [34]
    Zhou, A. J., Yao, A. B., Guo, Y. W., et al., Incremental network quantization: Towards lossless cnns with low-precision weights, ICLR, 2017, arXiv: 1702.03044.Google Scholar
  35. [35]
    Zhu, C. Z., Han, S., Miao, H. Z. and Dally, W. J., Trained ternary quantization, ICLR, 2017. arX-iv:1612.01064.Google Scholar

Copyright information

© The Editorial Office of CAM and Springer-Verlag Berlin Heidelberg 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of CaliforniaLos Angeles, Westwood, Los AngelesUSA
  2. 2.Department of AnthropologyUniversity of CaliforniaLos Angeles, Westwood, Los AngelesUSA
  3. 3.Department of MathematicsUniversity of CaliforniaIrvine, IrvineUSA

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