1. 6/3/2015 T.K. Cocx, tcocx@liacs.nl Prediction of criminal careers through 2- dimensional Extrapolation W. Kosters et al.

2. Prediction of criminal careers through 2-dimensional extrapolation 6/3/2015T.K. Cocx, tcocx@liacs.nl2 ?

3. Prediction of criminal careers through 2-dimensional extrapolation 6/3/2015T.K. Cocx, tcocx@liacs.nl3 ? ? 2-Dimensional Extrapolation

4. Prediction of criminal careers through 2-dimensional extrapolation 6/3/2015T.K. Cocx, tcocx@liacs.nl4 Research Area Criminal Career Study Sociology Psychology Criminology Law Computer Science

5. Prediction of criminal careers through 2-dimensional extrapolation 6/3/2015T.K. Cocx, tcocx@liacs.nl5 Criminal Careers

6. Prediction of criminal careers through 2-dimensional extrapolation 6/3/2015T.K. Cocx, tcocx@liacs.nl6 Analysis Goal Analysis

7. Prediction of criminal careers through 2-dimensional extrapolation 6/3/2015T.K. Cocx, tcocx@liacs.nl7 Practical Factors NatureDurationFrequencySeriousness

8. Prediction of criminal careers through 2-dimensional extrapolation 6/3/2015T.K. Cocx, tcocx@liacs.nl8 Paradigm Four factors Distance Measure Clustering Prediction Strategic analysis done on this

9. Prediction of criminal careers through 2-dimensional extrapolation 6/3/2015T.K. Cocx, tcocx@liacs.nl9 Alignment

10. Prediction of criminal careers through 2-dimensional extrapolation 6/3/2015T.K. Cocx, tcocx@liacs.nl10 Calculating Distance between Careers  Nature  Severity

11. Prediction of criminal careers through 2-dimensional extrapolation 6/3/2015T.K. Cocx, tcocx@liacs.nl11 Clustering and classification  Clustering is done based upon distance  Form of multi-dimensional scaling  Iterative is necessary  After clustering: classes are assigned to visible clusters.  By hand  11 classes  Classification can be done by k-means

12. Prediction of criminal careers through 2-dimensional extrapolation 6/3/2015T.K. Cocx, tcocx@liacs.nl12 Results: Clustering and Classification Year 1Year 2Year 3 Year 4

13. Prediction of criminal careers through 2-dimensional extrapolation 6/3/2015T.K. Cocx, tcocx@liacs.nl13 2-Dimensional Extrapolation ? Year 1 Year 2 Year 3 Year 4  The ‘Marble in Funnel’ and the ‘Criminal Career Prediction’ are two variants of the same problem:  Extrapolation of a time sequence in a plane.

14. Prediction of criminal careers through 2-dimensional extrapolation 6/3/2015T.K. Cocx, tcocx@liacs.nl14 Regular Mathematical Extrapolation  One variable (usually time, x) is given.  One Variable (Value, Temperature, weight, etc, y) is dependant on the given variable

15. Prediction of criminal careers through 2-dimensional extrapolation 6/3/2015T.K. Cocx, tcocx@liacs.nl15 2-Dimensional Extrapolation  One variable (usually time, t) is given.  Two variables (x, y) are dependant on the given variable.  Sometimes (as in the criminal career prediction) x and y are meaningless. Only the location relative to already placed elements is important.  Relatively under-researched area in mathematics.

16. Prediction of criminal careers through 2-dimensional extrapolation 6/3/2015T.K. Cocx, tcocx@liacs.nl16 Possible solutions 2-Dimensional Extrapolation Assume y depends on x Rotate image to optimally Arrange t-order on x-axis Regular second degree extrapolation Same as Left option Regular third degree extrapolation Assume x depends on t and y depends on t separately Extrapolate separately Combine in {x,y}-system Spline interpolate items t and t+1 Extrapolate after t last Different methods

17. Prediction of criminal careers through 2-dimensional extrapolation 6/3/2015T.K. Cocx, tcocx@liacs.nl17 Spline Extrapolation  There are two choices in spline extrapolation: Straight line cont. Polynomial cont.

18. Prediction of criminal careers through 2-dimensional extrapolation 6/3/2015T.K. Cocx, tcocx@liacs.nl18 Future Class Calculation  Select n existing data points closest to extrapolated curve.  The closer to ‘last known’ point, the more accurate.  Calculate expected attributes of individual under consideration with weighted average of the n points.  Classify current individual using these attributes.

19. Prediction of criminal careers through 2-dimensional extrapolation 6/3/2015T.K. Cocx, tcocx@liacs.nl19 Overview of method Two-dimensionalHigh-dimensional Four factors Distance Matrix Crimes committed Clustering Classification Extrapolation Class Prediction Prediction # crimes Combined

20. Prediction of criminal careers through 2-dimensional extrapolation 6/3/2015T.K. Cocx, tcocx@liacs.nl20 Implementation

21. Prediction of criminal careers through 2-dimensional extrapolation 6/3/2015T.K. Cocx, tcocx@liacs.nl21 Cluster Reduction

22. Prediction of criminal careers through 2-dimensional extrapolation 6/3/2015T.K. Cocx, tcocx@liacs.nl22 Results  Using the original Dutch National Criminal Record Database (App. 1 million offenders)

23. Prediction of criminal careers through 2-dimensional extrapolation 6/3/2015T.K. Cocx, tcocx@liacs.nl23 Effects of number of reference points  How many reference points are needed?  30-50 is enough

24. Prediction of criminal careers through 2-dimensional extrapolation 6/3/2015T.K. Cocx, tcocx@liacs.nl24 Effects of known years  How many years should be known for an accurate prediction?  3-5 is enough

25. Prediction of criminal careers through 2-dimensional extrapolation 6/3/2015T.K. Cocx, tcocx@liacs.nl25 Privacy issues  Data mining  general truth from lot of data  In this case translate this truth to individual cases  privacy and statistical issues arise  Comparable to data mining on financial transactions  Seen as acceptable  Reasonably few false positives  Operatives familiar with percentages  The approach poses no risk to non-offenders  only (existing) career continuation

26. Prediction of criminal careers through 2-dimensional extrapolation 6/3/2015T.K. Cocx, tcocx@liacs.nl26 Conclusion  Criminal career analysis can serve as basis for career prediction.  Using the concept of 2-dimensional extrapolation on an existing clustering yields the movement in time of an individual from his past to his future  Using ‘straight line spline’ extrapolation with the maximum existing elements predicts the future class of an offender with an 88.7% Accuracy.

27. Prediction of criminal careers through 2-dimensional extrapolation 6/3/2015T.K. Cocx, tcocx@liacs.nl27 Interrogation