6/3/2015 T.K. Cocx, [email protected] Prediction of criminal careers through 2- dimensional...

04/18/23

T.K. Cocx, [email protected]

Prediction of criminal careers through 2-dimensional Extrapolation

W. Kosters et al.

04/18/23 T.K. Cocx, [email protected] 2

Prediction of criminal careers through 2-dimensional extrapolation

?



?

?

2-Dimensional Extrapolation



Research Area

Criminal Career Study

Sociology

Psychology

Criminology

Law

ComputerScience



Criminal Careers



Analysis Goal

Analysis



Practical Factors

Nature DurationFrequency Seriousness



Paradigm

Four factors

Distance Measure

Clustering

Prediction

Strategic analysis done on this



Alignment



Calculating Distance between Careers

Nature Severity



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



Results: Clustering and Classification

Year 1

Year 2

Year 3

Year 4

Year 4

Year 4




?

Year 1

Year 2

Year 3Year 4

Year 4

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.



Regular Mathematical Extrapolation

One variable (usually time, x) is given. One Variable (Value, Temperature, weight, etc,

y) is dependant on the given variable




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.



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

Assume x depends on t and y dependson t separately

Extrapolate separately Combine in {x,y}-system

Spline interpolate items t and t+1 Extrapolate after tlast

Different methods



Spline Extrapolation

There are two choices in spline extrapolation:

Straight line cont. Polynomial cont.



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.



Overview of methodTwo-dimensional High-dimensional

Four factors

Distance Matrix

Crimes committed

Clustering

ClassificationExtrapolation

Class PredictionPrediction # crimes

Combined



Implementation



Cluster Reduction



Results Using the original Dutch National Criminal

Record Database (App. 1 million offenders)



Effects of number of reference points

How many reference points are needed?

30-50 is enough



Effects of known years

How many years should be known for an accurate prediction?

3-5 is enough



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



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.



Interrogation

6/3/2015 T.K. Cocx, [email protected] Prediction of criminal careers through 2- dimensional...

Documents

Transcript of 6/3/2015 T.K. Cocx, [email protected] Prediction of criminal careers through 2- dimensional...