Figure 1.
Density of eigenvalues of the correlation matrix of types of crimes associated with (i) the original data (top panel); (ii) 100 random shufflings of the database mimicking pure generalists (middle panel); and (iii) 100 random shufflings of the database mimicking pure specialists (bottom panel).
The largest eigenvalue of the empirical correlation matrix, which accounts for the generalist behavior of suspects, is about two third of the corresponding eigenvalue in the case of pure generalists, and about two times the one obtained for pure specialists. The second largest eigenvalue of the empirical correlation matrix, which suggests the presence of clusters of types of crimes, and therefore the presence of specialists in the set of suspects, is also intermediate between the corresponding ones obtained for pure generalists and pure specialists.
Figure 2.
Components of the eigenvector corresponding to the first eigenvalue of the correlation matrix of types of crimes for the original data, and average components of the first eigenvector over 100 independent realizations of the generalists' and specialists' shufflings.
In the latter cases, error bars correspond to one standard deviation over 100 realizations. The color of a spot indicates the chapter of the penal code of types of crimes belonging to the 6 most populated chapters. Specifically, we label types of crimes as follows: chapter 8 - theft, robbery and other types of crimes of stealing as blue (102 crimes), chapter 3 - types of crimes against life and health as red (60 crimes), chapter 9 - fraud and other acts of dishonesty as cyan (22 crimes), chapter 6 - sexual offences as violet (21 crimes), offences against the environmental code as orange (19 crimes), and chapter 4 - types of crimes against liberty and peace as green (17 crimes). In the case of generalists' and specialists' simulations we also show the interval of plus and minus one standard deviation around the average value. Types of crimes are ordered according to their occurrence in the database as shown in the bottom panel of the figure.
Figure 3.
Interrelations of clusters of the FDR statistically validated network of types of crimes.
The weight of a link between any two clusters is a monotonic increasing function of the sum of all the weights of links bridging types of crimes of the two clusters. The size of the node associated with each cluster of types of crimes is proportional to the number of suspects involved (see Table 1) in that cluster.
Table 1.
Characterization of clusters in the FDR network of crime types.
Table 2.
Mean value of the number of visited clusters of crime types.