17.1 Introduction. Giulia Massini and Massimo Buscema

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1 Chapter 17 Auto-Contractive Maps and Minimal Spanning Tree: Organization of Complex Datasets on Criminal Behavior to Aid in the Deduction of Network Connectivity Giulia Massini and Massimo Buscema 17.1 Introduction The aim of this chapter is to show how it is possible to organize a database of substantial size so as to be able to effectively control the information contained within it and therefore be able to make valid deductions that identify possible connections between the subjects. For example, let us assume we are analyzing a human population and have to deduce, on the basis of data concerning the individual subjects, which persons in actual fact associate with one another. The aim of this analysis is similar: having data on individuals whose criminal history has been archived, but concerning whom it is not known, or at any rate it is not recorded within this archive, if any relationship exists between them. In short, one must find some mechanism by which it can be determined those individuals for whom a relationship does exist. For example, to determine if they are part of the same gang or at any rate whether they are involved in the same drug trafficking circle. We referred to a database that is part of the Metropolitan Police Service Central Drug Trafficking Database (CDTD), which has already been analyzed elsewhere in this book, consisting of 1,120 subjects who had been arrested in connection with drugs in various boroughs of London each identified by 144 variables. 1 For each person, they involve the following profiles: Sex(male, female, not known) Borough of residence of the subject arrested (32 boroughsc 1 NotAvailable) 1 This dataset was extracted in June 2006 when the CDTD Database contained 1,590 tactic sequences, 1,667 persons and 1,190 accused persons (and also 70 incomplete cases). G. Massini ( ) M. Buscema Semeion Research Center of Sciences of Commuication, via Sersale 117, Rome, Italy g.massini@semeion.i M. Buscema and W.J. Tastle (eds.), Intelligent Data Mining in Law Enforcement Analytics: New Neural Networks Applied to Real Problems, DOI / , Springer ScienceCBusiness Media Dordrecht

2 400 G. Massini and M. Buscema Borough where each subject was arrested Arrest Place (32 boroughsc 1NotAvailable) Nationality of the subject arrested (Africa AFR, Asia ASIA, Eastern Europe EASTEU, Europe EU, Ireland IRE, Jamaica JAM, ME, NK, SAME, Turkey and Sylon TU-CY, United Kingdom UK, Vietnam VTN) The somatic stock of the subject arrested (White European EA1, Dark European EA2, Afro-Caribbean EA3, Asian EA4, Oriental EA5, Arab EA6) Age (expressed in six classes: <18, 18 21, 21 25, 25 35, 35 45, >45) Number of previous convictions Number of previous offenses Details of the previous offenses (FirstConvAge, LastConvAge, Drug, TheftKindred, AgainstPerson, OffensiveWeapons, Sexual, RelatedToPolice, Fraud, Total, AgainstProperty) Number of previous arrests Details of previous arrests (Theft and Kindred offenses, offenses the Person offenses, Drug Trafficking offenses, Drug Possession offenses, Other Drug offenses, Offensive Weapon offenses, Firearms offenses, Kidnapping and Abduction offenses, Other Violent offenses, Other offenses) Number of drug seizures Type of drugs seized from the subject arrested (Cannabis, Cocaine, Crack, Heroin/Diamorphine, MDMA) Amount of money found in their possession at the time of the arrest (NumOf- CashSeizures, Pounds) Number of tactics used by the police (NumOfTactics) Type of agent who made the arrest (Police, Non-Law Enforcement Agent, Other Law Enforcement Agent) Types of tactics used by the police to make the arrest (Search of Object, Search of Person, Search of Premises, Covert Purchase, Controlled Delivery, Other Generic Tactic) Number of tactic sequences Arrest made as part of a more widely organized operation (InOperation) Aims of the police operations Arrest Mode (Direct, Result of Enquiries, Given into Custody, Other, not defined NA) Behavior of the person at the time of the arrest, whether or not violent Whether at the time of the arrest the subject was on bail Upon close inspection of the above attributes, it can be seen that there is no explicit information connecting the subjects with one another, but there does exist, for each subject, a summation of his illicit drug activities. It is with this connection, that of drug activity, to which each variable is assigned that characterizes the sum of all the crimes that the subject has committed rather than to an assignment of individual crimes to an individual. This distinction is subtle, but critical.

3 17 Auto-Contractive Maps and Minimal Spanning Tree: Organization Method The procedure used to attain the objective consists of three main steps (Kruskal 1956): 1. Processing of the data by an Auto-Contractive Map network that fixes the distance between the various records of the DB and each record with all the others (CS SW, ver.5.0 Semeion ) 2. Identification of the connections between the records, based on the distances identified by the Auto-Contractive Map, by the minimal spanning tree, MST (MST Detector SW, ver.3.0 Semeion 2006) 3. Creation of the graph that visualizes the relationships between the records identified by the MST (Tree Visualizer SW, ver.1.0 Semeion 2006) In the MST tree graph, the leaves (also called nodes) are the individual points that represent the 1,120 records contained in the database and can therefore be associated with an individual physical person, while the relationships between the records are represented by the branches lines (also called edges). In Fig. 17.1, we show a visualization of the overall graph. Fig MST graph produced by the Tree Visualizer SW ver.1.0 Semeion 2006 from the data of 1,120 persons arrested in London for drug trafficking processed by CS SW, ver.5.0 Semeion

4 402 G. Massini and M. Buscema From an analysis of the graph, it was possible to establish, as we shall later see, that the complexity of the information contained in it, given by the high number of subjects and variables, has been organized effectively for classifying the subjects and making deductions concerning the possible meanings that can be attributed to the connections between them Organization of the Subjects of the DB on the MST with Respect to the Variables Some variables are used in the system as guidelines for carrying out a complex classification of the DB, that is, sex (Fig. 17.2), age (Fig. 17.3), nationality (Fig. 17.4), and ethnicity (Fig. 17.5); with respect to these individual variables, the subjects have been placed in specific branchings. The variable sex (male/female/not known) sees female subjects distributed together with the not known subjects on a branch that starts from an area close to the central point of the graph (in the graph, the central point is represented in red and the variable of interest is in green), while the male subjects are distributed throughout the remainder of the graph. Also with respect to the variable age (Fig. 17.3), the system was able to combine the subjects into groups. One can observe that persons aged between 25 and 35 occupy the center of the graph insofar as men are concerned. However, the subjects belonging to the other age bands are positioned in groups that leave from the center and are arranged into areas that are more or less peripheral in relation to their nationality and/or ethnicity. This suggests that the age between 25 and 35 is the most active phase of the subject s criminal life in this area and a point at which the subject opens up new criminal contacts in the drugs network. It should also be noted that the age between 25 and 35 years is the age that contains the greatest number of Fig The figure shows the distribution of the 1,120 subjects according to sex

5 17 Auto-Contractive Maps and Minimal Spanning Tree: Organization subjects, as the following histogram shows, where the curve is at a maximum in this age band. 400 age (<18) (18-21) (21-25) (25-35) (35-45) (>45) Histogram of the distribution of criminal subjects based on age Histogram of the distribution of criminal subjects based on age Regarding nationality, a macro-group is identified (Fig. 17.4) positioned centrally and consisting of 723 British subjects (UK). These subjects belong to various ethnic groups of which the most important at the strategic level for drug trafficking is, by this analysis, assigned to Afro-Caribbeans having British nationality and aged between 25 and 35 years (Fig. 17.5). With regard to ethnicity, it is seen that the two groups opposite in the graph are Afro-Caribbean/White European. It was possible, therefore, to identify this central group in the MST graph by querying the system and placing the operator <AND> between the variables sex, age, nationality, and ethnicity (Fig. 17.6) Deductions Concerning the Relationships Between the Subjects To verify whether the system had actually connected the subjects of the present DB in real mode, a comparison was made with other data belonging to the same subjects but relating to the CRIS archive. The CRIS (Central Drug Trafficking Database) is the original source archive of the current DB, having more extensive information on the subjects. Some of this additional information concerns data that establishes the relationship between subjects. In the CRIS, it was possible to find information on subjects who had been arrested in the same police operation or who had a degree of relationship with others, etc.

6 404 G. Massini and M. Buscema Fig The figure shows the distribution of the subjects according to their age band It was therefore possible to establish that some of the subjects who were connected in the CRIS were in a position of proximity on the branchings of the MST graph. Since the CRIS contains only information that proves the actual relationship between the subjects, it may be hoped that the MST tree might suggest other possible relationships between the subjects, even if they have not emerged explicitly through the information already in the possession of the police. Next, we show some examples of the information present in the CRIS on the connection between the subjects and concerning which it was found that in the MST graph, these subjects were placed in a relationship of proximity in specific branchings. For each example, the following information is defined: Image of the overall graph and identification of the branch where the subjects who were connected in the CRIS are identified Zoom onto the branch selected and identification of the subjects

7 17 Auto-Contractive Maps and Minimal Spanning Tree: Organization Fig The figure shows the distribution of the subjects according to their nationality List of the common variables that characterize the subjects in the current DB Comments on the information obtained by consulting the CRIS In this example (Fig. 17.7), we show the positioning on the MST of some subjects who the CRIS had connected with one another and who in the MST are placed close to the base of common branchings. The information shared for these subjects is possession of Cannabis at the time of the arrest. However, other information can be found in the CRIS that provides a connection between pairs of individuals: 84 and 137, 137 and 463, 463 and 624, 137 and 624. Subjects 84 and 137 were both in possession of weapons. Subject 137 was also linked to 463 because both were involved in growing Cannabis. Subject 463 was in turn also connected in the CRIS to 624 in a strange way in that they were both

8 406 G. Massini and M. Buscema Fig The figure shows the distribution of the subjects according to their ethnicity (somatic stock) caught with Cannabis hidden in a bag of dirty laundry. Obviously, this information on the hiding place was not present in the DB on which the present MST is based. Subject 137 was also connected to 624, both being found in possession of Cannabis during execution of a warrant. In this branch (Fig. 17.8), a connection was established between subjects 191 and 196 in that the CRIS had information concerning the fact that both had been located by CCTV (closed-circuit television) and were arrested in Coldharbour Lane, Lambeth. This information was also not present in the current DB.

9 17 Auto-Contractive Maps and Minimal Spanning Tree: Organization Fig The figure on the left shows the distribution of the subjects having certain characteristics (UK/male/25 35 years); the one on the right shows a selection made from the former when a further characteristic is activated: Afro-Caribbean ethnicity Fig The figure shows the positioning on the MST graph of subjects focused on in the comparison with the data from the CRIS

10 408 G. Massini and M. Buscema Fig The figure shows the positioning on the MST graph of subjects focused on in the comparison with the data from the CRIS In the CRIS data, connections can be identified between subjects 164, 183, and 557 (Fig. 17.9) in that they were arrested as a result of special police surveillance, for example, with CCTV (closed-circuit television), which had targeted them specifically. It also emerged that all these episodes occurred in Camden. In the CRIS, similarities can be found between subjects 140, 566, and 602: they were all arrested in Lambeth. The police had got to them indirectly as a result of other investigations, not having identified them previously. One had been identified as a result of enquiries at the home of a missing girl, the other when executing a warrant for another case, and lastly offering drugs in plain clothes. From the CRIS reports for persons 200, 528, 561, 806, 1,292, and 1,438 (Fig ), it emerged that all shared a common characteristic; that is, of all the drug seizures it should be noted that none were the result of police action based on tests but rather the result of the execution of a warrant through a person of trust in a previous arrest who warned the police. All were found in possession of MDMA. Furthermore, 50% of them were arrested in nightclubs, although not the same one, but in clubs in different areas.

11 17 Auto-Contractive Maps and Minimal Spanning Tree: Organization Fig The figure shows the positioning on the MST graph of subjects focused on in the comparison with the data from the CRIS In the CRIS report, it is established that persons 779 and 781 are brothers (Fig ) who had been arrested together in the same tactic sequence. This information was not present in the DB that enabled the MST graph to be drawn up. This example (Fig ) is very similar to the previous one. In fact, in the CRIS report, it is established that persons 350 and 352 are brothers. Clearly, in this case too, appropriate data was not present in the DB that enabled the MST graph to be drawn up. In the CRIS reports, it emerges that subjects 475, 476, 477, and 1,317 (Fig ) are linked in that they are part of the same Middle Market Drug Project and were arrested together. Subject 1,312 is also linked in that, although not part of the same operation, he is nevertheless part of the Middle Market Drug Project. Subject 1,445 is linked to these in that he was arrested with a warrant in a National Crime Squad operation. Absolutely none of this information was present in the DB that allowed the MST graph to be drawn up, yet their relationships are nonetheless defined in the graphs.

12 410 G. Massini and M. Buscema Fig The figure shows the positioning on the MST graph of subjects focused on in the comparison with the data from the CRIS Fig The figure shows the positioning on the MST graph of subjects focused on in the comparison with the data from the CRIS

13 17 Auto-Contractive Maps and Minimal Spanning Tree: Organization Fig The figure shows the positioning on the MST graph of subjects focused on in the comparison with the data from the CRIS 17.5 Conclusion We conclude with this very significant example with some observations. The system that we used was capable of identifying the connections between records, even though the presence of an explicit connection was not available in the data. This gives us pause to consider the possibility that other identifiable connections are real even if they not are known at the moment and are not present in the CRIS archive. This leads us to a thought to ponder: how does one interpret all the connections present on the graph? The conceptual system on which the MST is based is that the Auto CM networks carry out a global evaluation of the whole of the DB and assign a value to the connection between each record individually with respect to all the others. By this operation, the solution space has a dimensionality equal to the number of the records (in this case 1,120), and each record contracts and/or expands the space that separates it from the others. The resultant topology is stored on the connections matrix that links each record with all the others. Thus, at the end, a numerical value is assigned representing each relationship between pairs of records. This value is inversely proportional to the strength of relationship between these two records: smaller if the relationship between the records is very strong, greater if the relationship is weak. Therefore, the MST acts on all these values and selects one

14 412 G. Massini and M. Buscema Fig The figure shows the positioning on the MST graph of subjects focused on in the comparison with the data from the CRIS for each record that shows the strongest relationship contributed to the economy of the global graph whose length must be the smallest possible. The final graph must, by definition, be completely connected (i.e., to a single graph) and not have circuits between the branches. Thus, the MST has as an obligatory link between each record representing the single choice made from among all those possible. However, in the graph, it is apparent that a node can be connected to many others, since several records can maintain the strongest relationship, that is, a tie, with the same node. It is likely that this system may be useful for suggesting alternative routes to investigate for a better understanding of the dynamic existing in drug trafficking. References Kruskal, J. B. (1956). On the shortest spanning subtree of a graph and the traveling salesman problem. Proceedings of the American Mathematical Society, 7(1), Massimo, B., & Sacco, P. L. (2010). Auto-contractive maps, the H function, and the maximally regular graph (MRG): a new methodology for data mining (chapter 11). In V. Capecchi et al. (Eds.), Applications of mathematics in models, artificial neural networks and arts. Dordrecht/London: Springer. doi: /

15 17 Auto-Contractive Maps and Minimal Spanning Tree: Organization Software Buscema, M. (2007). Contractive Maps. Software for programming Auto Contractive Maps (Semeion Software #15, v. 2), Rome. Buscema, M. (2007). Constraints Satisfaction Networks. Software for programming Non Linear Auto-Associative Networks, Semeion Software #14 (v. 10), Rome. Buscema, M. (2008). MST. Software for programming Trees from artificial networks weights matrix (Semeion Software #38, v 5), Rome. Massini, G. (2007). Tree Visualizer. Software to draw and manipulate tree graph (Semeion Software #40, v. 3), Rome.