Prediction of Crime/Terrorist Event Locations National Defense and Homeland Security: Anomaly...
-
Upload
lauren-dowd -
Category
Documents
-
view
215 -
download
0
Transcript of Prediction of Crime/Terrorist Event Locations National Defense and Homeland Security: Anomaly...
![Page 1: Prediction of Crime/Terrorist Event Locations National Defense and Homeland Security: Anomaly Detection Francisco Vera, SAMSI.](https://reader035.fdocuments.in/reader035/viewer/2022081602/55151d0f550346c77d8b502d/html5/thumbnails/1.jpg)
Prediction of Crime/Terrorist Event Locations
National Defense and Homeland Security: Anomaly Detection
Francisco Vera, SAMSI
![Page 2: Prediction of Crime/Terrorist Event Locations National Defense and Homeland Security: Anomaly Detection Francisco Vera, SAMSI.](https://reader035.fdocuments.in/reader035/viewer/2022081602/55151d0f550346c77d8b502d/html5/thumbnails/2.jpg)
Outline
• Introduction
• Location space and feature space
• The model
• Feature selection
• Examples
• Evaluation/comparison of models
• Discussion
![Page 3: Prediction of Crime/Terrorist Event Locations National Defense and Homeland Security: Anomaly Detection Francisco Vera, SAMSI.](https://reader035.fdocuments.in/reader035/viewer/2022081602/55151d0f550346c77d8b502d/html5/thumbnails/3.jpg)
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
![Page 4: Prediction of Crime/Terrorist Event Locations National Defense and Homeland Security: Anomaly Detection Francisco Vera, SAMSI.](https://reader035.fdocuments.in/reader035/viewer/2022081602/55151d0f550346c77d8b502d/html5/thumbnails/4.jpg)
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
![Page 5: Prediction of Crime/Terrorist Event Locations National Defense and Homeland Security: Anomaly Detection Francisco Vera, SAMSI.](https://reader035.fdocuments.in/reader035/viewer/2022081602/55151d0f550346c77d8b502d/html5/thumbnails/5.jpg)
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
![Page 6: Prediction of Crime/Terrorist Event Locations National Defense and Homeland Security: Anomaly Detection Francisco Vera, SAMSI.](https://reader035.fdocuments.in/reader035/viewer/2022081602/55151d0f550346c77d8b502d/html5/thumbnails/6.jpg)
Location Space
North
East
Cops
I-40
I-85
![Page 7: Prediction of Crime/Terrorist Event Locations National Defense and Homeland Security: Anomaly Detection Francisco Vera, SAMSI.](https://reader035.fdocuments.in/reader035/viewer/2022081602/55151d0f550346c77d8b502d/html5/thumbnails/7.jpg)
Feature Space
Highway
Cops
![Page 8: Prediction of Crime/Terrorist Event Locations National Defense and Homeland Security: Anomaly Detection Francisco Vera, SAMSI.](https://reader035.fdocuments.in/reader035/viewer/2022081602/55151d0f550346c77d8b502d/html5/thumbnails/8.jpg)
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)
![Page 9: Prediction of Crime/Terrorist Event Locations National Defense and Homeland Security: Anomaly Detection Francisco Vera, SAMSI.](https://reader035.fdocuments.in/reader035/viewer/2022081602/55151d0f550346c77d8b502d/html5/thumbnails/9.jpg)
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
![Page 10: Prediction of Crime/Terrorist Event Locations National Defense and Homeland Security: Anomaly Detection Francisco Vera, SAMSI.](https://reader035.fdocuments.in/reader035/viewer/2022081602/55151d0f550346c77d8b502d/html5/thumbnails/10.jpg)
The Model
• Times:• Locations:• Features:• Transition density:
![Page 11: Prediction of Crime/Terrorist Event Locations National Defense and Homeland Security: Anomaly Detection Francisco Vera, SAMSI.](https://reader035.fdocuments.in/reader035/viewer/2022081602/55151d0f550346c77d8b502d/html5/thumbnails/11.jpg)
The Model
• Spatial transition density• Temporal transition density• Assumption: Temporal transition does not
depend on spatial transition
![Page 12: Prediction of Crime/Terrorist Event Locations National Defense and Homeland Security: Anomaly Detection Francisco Vera, SAMSI.](https://reader035.fdocuments.in/reader035/viewer/2022081602/55151d0f550346c77d8b502d/html5/thumbnails/12.jpg)
The Model
![Page 13: Prediction of Crime/Terrorist Event Locations National Defense and Homeland Security: Anomaly Detection Francisco Vera, SAMSI.](https://reader035.fdocuments.in/reader035/viewer/2022081602/55151d0f550346c77d8b502d/html5/thumbnails/13.jpg)
The Model
![Page 14: Prediction of Crime/Terrorist Event Locations National Defense and Homeland Security: Anomaly Detection Francisco Vera, SAMSI.](https://reader035.fdocuments.in/reader035/viewer/2022081602/55151d0f550346c77d8b502d/html5/thumbnails/14.jpg)
The Model
![Page 15: Prediction of Crime/Terrorist Event Locations National Defense and Homeland Security: Anomaly Detection Francisco Vera, SAMSI.](https://reader035.fdocuments.in/reader035/viewer/2022081602/55151d0f550346c77d8b502d/html5/thumbnails/15.jpg)
Feature Selection
![Page 16: Prediction of Crime/Terrorist Event Locations National Defense and Homeland Security: Anomaly Detection Francisco Vera, SAMSI.](https://reader035.fdocuments.in/reader035/viewer/2022081602/55151d0f550346c77d8b502d/html5/thumbnails/16.jpg)
Feature Selection
![Page 17: Prediction of Crime/Terrorist Event Locations National Defense and Homeland Security: Anomaly Detection Francisco Vera, SAMSI.](https://reader035.fdocuments.in/reader035/viewer/2022081602/55151d0f550346c77d8b502d/html5/thumbnails/17.jpg)
Feature Selection• Second paper mentions:
– Use of the correlation structure to drop variables– Principal Components
![Page 18: Prediction of Crime/Terrorist Event Locations National Defense and Homeland Security: Anomaly Detection Francisco Vera, SAMSI.](https://reader035.fdocuments.in/reader035/viewer/2022081602/55151d0f550346c77d8b502d/html5/thumbnails/18.jpg)
![Page 19: Prediction of Crime/Terrorist Event Locations National Defense and Homeland Security: Anomaly Detection Francisco Vera, SAMSI.](https://reader035.fdocuments.in/reader035/viewer/2022081602/55151d0f550346c77d8b502d/html5/thumbnails/19.jpg)
![Page 20: Prediction of Crime/Terrorist Event Locations National Defense and Homeland Security: Anomaly Detection Francisco Vera, SAMSI.](https://reader035.fdocuments.in/reader035/viewer/2022081602/55151d0f550346c77d8b502d/html5/thumbnails/20.jpg)
![Page 21: Prediction of Crime/Terrorist Event Locations National Defense and Homeland Security: Anomaly Detection Francisco Vera, SAMSI.](https://reader035.fdocuments.in/reader035/viewer/2022081602/55151d0f550346c77d8b502d/html5/thumbnails/21.jpg)
Features Selected
![Page 22: Prediction of Crime/Terrorist Event Locations National Defense and Homeland Security: Anomaly Detection Francisco Vera, SAMSI.](https://reader035.fdocuments.in/reader035/viewer/2022081602/55151d0f550346c77d8b502d/html5/thumbnails/22.jpg)
Example
![Page 23: Prediction of Crime/Terrorist Event Locations National Defense and Homeland Security: Anomaly Detection Francisco Vera, SAMSI.](https://reader035.fdocuments.in/reader035/viewer/2022081602/55151d0f550346c77d8b502d/html5/thumbnails/23.jpg)
Gaussian Mixture Model
![Page 24: Prediction of Crime/Terrorist Event Locations National Defense and Homeland Security: Anomaly Detection Francisco Vera, SAMSI.](https://reader035.fdocuments.in/reader035/viewer/2022081602/55151d0f550346c77d8b502d/html5/thumbnails/24.jpg)
Weighted Product Kernel
![Page 25: Prediction of Crime/Terrorist Event Locations National Defense and Homeland Security: Anomaly Detection Francisco Vera, SAMSI.](https://reader035.fdocuments.in/reader035/viewer/2022081602/55151d0f550346c77d8b502d/html5/thumbnails/25.jpg)
Filter Product Kernel
![Page 26: Prediction of Crime/Terrorist Event Locations National Defense and Homeland Security: Anomaly Detection Francisco Vera, SAMSI.](https://reader035.fdocuments.in/reader035/viewer/2022081602/55151d0f550346c77d8b502d/html5/thumbnails/26.jpg)
Terrorist Events Example
![Page 27: Prediction of Crime/Terrorist Event Locations National Defense and Homeland Security: Anomaly Detection Francisco Vera, SAMSI.](https://reader035.fdocuments.in/reader035/viewer/2022081602/55151d0f550346c77d8b502d/html5/thumbnails/27.jpg)
Features Selected
![Page 28: Prediction of Crime/Terrorist Event Locations National Defense and Homeland Security: Anomaly Detection Francisco Vera, SAMSI.](https://reader035.fdocuments.in/reader035/viewer/2022081602/55151d0f550346c77d8b502d/html5/thumbnails/28.jpg)
Distance Features Only
![Page 29: Prediction of Crime/Terrorist Event Locations National Defense and Homeland Security: Anomaly Detection Francisco Vera, SAMSI.](https://reader035.fdocuments.in/reader035/viewer/2022081602/55151d0f550346c77d8b502d/html5/thumbnails/29.jpg)
Logistic Regression
![Page 30: Prediction of Crime/Terrorist Event Locations National Defense and Homeland Security: Anomaly Detection Francisco Vera, SAMSI.](https://reader035.fdocuments.in/reader035/viewer/2022081602/55151d0f550346c77d8b502d/html5/thumbnails/30.jpg)
Logistic Regression
![Page 31: Prediction of Crime/Terrorist Event Locations National Defense and Homeland Security: Anomaly Detection Francisco Vera, SAMSI.](https://reader035.fdocuments.in/reader035/viewer/2022081602/55151d0f550346c77d8b502d/html5/thumbnails/31.jpg)
Combination
![Page 32: Prediction of Crime/Terrorist Event Locations National Defense and Homeland Security: Anomaly Detection Francisco Vera, SAMSI.](https://reader035.fdocuments.in/reader035/viewer/2022081602/55151d0f550346c77d8b502d/html5/thumbnails/32.jpg)
Evaluation/Comparison of Models
![Page 33: Prediction of Crime/Terrorist Event Locations National Defense and Homeland Security: Anomaly Detection Francisco Vera, SAMSI.](https://reader035.fdocuments.in/reader035/viewer/2022081602/55151d0f550346c77d8b502d/html5/thumbnails/33.jpg)
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?
)else everywherean greater th is at density ()()()(
sPdxxfpsfxf
s
![Page 34: Prediction of Crime/Terrorist Event Locations National Defense and Homeland Security: Anomaly Detection Francisco Vera, SAMSI.](https://reader035.fdocuments.in/reader035/viewer/2022081602/55151d0f550346c77d8b502d/html5/thumbnails/34.jpg)
Crime Example
![Page 35: Prediction of Crime/Terrorist Event Locations National Defense and Homeland Security: Anomaly Detection Francisco Vera, SAMSI.](https://reader035.fdocuments.in/reader035/viewer/2022081602/55151d0f550346c77d8b502d/html5/thumbnails/35.jpg)
Crime Example
![Page 36: Prediction of Crime/Terrorist Event Locations National Defense and Homeland Security: Anomaly Detection Francisco Vera, SAMSI.](https://reader035.fdocuments.in/reader035/viewer/2022081602/55151d0f550346c77d8b502d/html5/thumbnails/36.jpg)
Crime Example
![Page 37: Prediction of Crime/Terrorist Event Locations National Defense and Homeland Security: Anomaly Detection Francisco Vera, SAMSI.](https://reader035.fdocuments.in/reader035/viewer/2022081602/55151d0f550346c77d8b502d/html5/thumbnails/37.jpg)
Crime Example
![Page 38: Prediction of Crime/Terrorist Event Locations National Defense and Homeland Security: Anomaly Detection Francisco Vera, SAMSI.](https://reader035.fdocuments.in/reader035/viewer/2022081602/55151d0f550346c77d8b502d/html5/thumbnails/38.jpg)
Terrorist Example
![Page 39: Prediction of Crime/Terrorist Event Locations National Defense and Homeland Security: Anomaly Detection Francisco Vera, SAMSI.](https://reader035.fdocuments.in/reader035/viewer/2022081602/55151d0f550346c77d8b502d/html5/thumbnails/39.jpg)
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