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Prediction of Crime/Terrorist Event Locations

Prediction of Crime/Terrorist Event Locations. National Defense and Homeland Security: Anomaly Detection Francisco Vera, SAMSI. Outline. Introduction Location space and feature space The model Feature selection Examples Evaluation/comparison of models Discussion. Introduction.

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Prediction of Crime/Terrorist Event Locations

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  1. Prediction of Crime/Terrorist Event Locations National Defense and Homeland Security: Anomaly Detection Francisco Vera, SAMSI

  2. Outline • Introduction • Location space and feature space • The model • Feature selection • Examples • Evaluation/comparison of models • Discussion

  3. Introduction • Talk based on two papers • “Criminal incident prediction using a point-pattern-based density model” • By Hua Liu and Donald Brown • “Spatial forecast methods for terrorist events in urban environments” • By Donald Brown, Jason Dalton, and Heidi Hoyle • Same modeling approach in both papers

  4. Introduction • Hot spots: Criminal events tend to cluster in space. • Traditional methods look for clusters in space • Only coordinates, dates and times are used • Poor performance • Unable to predict new hot spots • Terrorist events are rare, do not cluster in space

  5. Introduction • Proposed method look for offender’s preferences in crime site selection • Instead of looking at the coordinates, look at the features of crime locations • Demographic, social, economic • Distance to key features • Closest police station • Closest highway • Closest convenience store

  6. North I-40 Cops I-85 East Location Space

  7. Highway Cops Feature Space

  8. Location Space and Feature Space • Transform observations from location space to feature space • Look for clusters in the feature space • Fit a density in feature space • For each coordinate, the likelihood of an event is the density of the transformed coordinate (from location to feature)

  9. Advantages • Better performance (issues with comparison) • Ability to predict new hot spots • Terrorist events do not cluster in location space, but they do in feature space

  10. The Model • Times: • Locations: • Features: • Transition density:

  11. The Model • Spatial transition density • Temporal transition density • Assumption: Temporal transition does not depend on spatial transition

  12. The Model

  13. The Model

  14. The Model

  15. Feature Selection

  16. Feature Selection

  17. Feature Selection • Second paper mentions: • Use of the correlation structure to drop variables • Principal Components

  18. Features Selected

  19. Example

  20. Gaussian Mixture Model

  21. Weighted Product Kernel

  22. Filter Product Kernel

  23. Terrorist Events Example

  24. Features Selected

  25. Distance Features Only

  26. Logistic Regression

  27. Logistic Regression

  28. Combination

  29. Evaluation/Comparison of Models

  30. Evaluation/Comparison of Models • The reasoning: Percentile scores should be larger at event points • Evaluate percentile scores at all event point and average. • Best model has highest average percentile score • Is this good?

  31. Crime Example

  32. Crime Example

  33. Crime Example

  34. Crime Example

  35. Terrorist Example

  36. Discussion • Feature space has advantages over location space • The Model: Decomposition of the transition density • Feature selection: Correlations, principal components, Gini index • Evaluation/comparison of models: Percentile score • Paper: Detecting local regions of change in high-dimensional or terrorist point processes, by Michael Porter and Donald Brown

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