1. Prediction of criminal careers through 2-dimensional Extrapolation
T.K. Cocx,
2/23/2019
W. Kosters et al.

2. ?
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3. 2-Dimensional Extrapolation? ?
2-Dimensional Extrapolation
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4. Research Area Criminal Career Study Computer Science Sociology
Psychology
Criminology
Law
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5. Criminal Careers
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6. Analysis Goal
Analysis
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7. Practical Factors Nature Frequency Seriousness Duration 2/23/2019
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8. Strategic analysis done on this
Paradigm
Four factors
Distance Measure
Strategic analysis done on this
Clustering
Prediction
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9. Alignment
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10. Calculating Distance between Careers
Nature
Severity
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11. Results: Clustering and Classification
Year 4
Year 3
Year 2
Year 1
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12. 2-Dimensional Extrapolation
The ‘Marble in Funnel’ and the ‘Criminal Career Prediction’ are two variants of the same problem:
Extrapolation of a time sequence in a plane.
Year 1
Year 2
Year 3
Year 4 ?
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T.K. Cocx,

13. Regular Mathematical Extrapolation
One variable (usually time, x) is given.
One Variable (Value, Temperature, weight, etc, y) is dependant on the given variable
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14. 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.
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T.K. Cocx,

15. 2-Dimensional Extrapolation
Possible solutions
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
2-Dimensional Extrapolation
Spline interpolate items t and t+1
Extrapolate after tlast
Different methods
Assume x depends on t and y depends on t separately
Extrapolate separately
Combine in {x,y}-system
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16. Spline Extrapolation
There are two choices in spline extrapolation: Straight line cont Polynomial cont.
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17. Future Class Calculation
Select n existing data points closest to extrapolated line.
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.
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18. Results
Using the original Dutch National Criminal Record Database (App. 1 million offenders)
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19. Comparison High-dim. Extrapolation
Speed increase with a factor 100.
Accuracy increase with 0.8 percentage points.
Multi-dimensional space is rather empty.
Classification is based upon a 2-dimensional clustering anyway.
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T.K. Cocx,

20. 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.
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21. Interrogation
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