Prediction of Crime/Terrorist Event Locations

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

21. Features Selected

22. Example

23. Gaussian Mixture Model

24. Weighted Product Kernel

25. Filter Product Kernel

26. Terrorist Events Example

27. Features Selected

28. Distance Features Only

29. Logistic Regression

30. Logistic Regression

31. Combination

32. Evaluation/Comparison of Models

33. 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?

34. Crime Example

35. Crime Example

36. Crime Example

37. Crime Example

38. Terrorist Example

39. 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