The spatial structure and typology of crime in Poland - an example of using validation of the number of clusters in k-means method

This paper presents an overview of the present state of crime in Poland, and the main goals are to detect the distribution and clustering of crimes, and to identify high rate regions. It is a common practice to compare countries, regions or cities in terms of safety performance, and to rank them in terms of risk indicators such as the crime rates, which are often expressed as the number of crime per 10 000 persons. This paper examines the subregional disparities hidden behind the national statistics (www.stat.gov.pl) on some crime statistics in Poland with GIS and spatial analyses. The first step to identify possible patterns of crime rates is to map the crime phenomenon. The distribution of relative rates of crimes in the Polish subregions were presented in fig. 1. The analysis of all the committed in Poland crimes in years 2008‒2011, maintaining the same territorial level of researches (66 subregions; i. e. NTS-3 European statistical level) revealed an interesting crime geographies picture, which in turn, increased the assumption of not homogenous spatial distributions. Talking into consideration all the crimes in Poland there were 294 crimes per 10 000 inhabitants, but in large cities (Wrocław – 561; katowicki – 527; trójmiejski – 509; Poznań ‒ 488) and in north-western subregions the value was more than 50% higher than the Polish average. In the eastern subregions the number of crimes was the half of the Polish average value (krośnieński – 169; przemyski – 174; rzeszowski ‒ 179). The changes of crime rates in 2008‒2011 years were shown in fig. 2. Statistics of growth rates in north subregions there was a more than 2% decrease (koszaliński, Szczecin, szczeciński, słupski, ełcki), in the central and southern subregions a strong increase (nearly 10%; nowosądecki, Kraków, poznański, tyski). The statistics for whole Poland indicates an increase of 2%. If the number of solved crimes is related to the estimated total number of crimes, the performance of police is very weak – generally in Poland it is only about 70%. In the subregions of largest Polish cities, detectability of crimes is much lower in comparison to other subregions (fig. 3). Crimes can be distinguished by four categories: criminal offences (the main two groups are: against property and against life and health), commercial crimes, traffic and the so-called “others”. In this paper, some kinds of crime activities were examined. Criminal crimes against life and health include crimes like homicide, deliberate wounding, assault, damage to health. Assaults and damages to health are, in general, committed by male adults; in recent years, more types of violent crimes are committed by the underaged. The subregions of Śląsk, West and North Poland, had relatively more violent crimes per 10 000 population (fig. 5). Category of crimes against property consists of various forms of theft, burglary and robbery, theft with assault, criminal coercion. Crimes against property account for 53% of total crimes and for 78% of criminal offences. In general, property crimes per 10 000 residents are strongly overrepresented in the crime profiles of the subregions of West and North Poland, Śląsk region (katowicki – 351; gliwicki ‒ 256) and all largest Polish cities (trójmiejski – 303; Kraków – 292; Poznań ‒ 291), but typically lower in the subregions of East (puławski ‒ 72; przemyski – 72; chełmsko-zamojski – 77; krośnieński) and Central (sieradzki) Poland (fig. 6). Commercial crime is the crime of “respectable” people. There is a very broad rande of examples of white-collar crime. Individuals (for example computer criminals, taxes), small businesses (for example VAT taxes), large corporations (for example creative bookkeeping), and governmental agencies (for example corruption) may get involved. Some researchers argue that commercial crime is even more serious than, the violent acts of the street criminals, because is like an insidious corrosion that slowly but surely destroys national economy. White-collar crimes per 10 000 people are overrepresented in subregions which are located in different parts of Poland, such as: Trójmiasto (161 crimes), sandomiersko-jędrzejowski (82), katowicki (74), bytomski, gorzowski and bydgosko-toruński (fig. 7). Traffic crimes – Polish law distinguishes between traffic violations (for example, driving at higher speeds than allowed, driving without a licence, or ignoring red traffic lights) and more serious traffic crimes, e.g. alcohol driving, accidents with victims, hit-and-run accidents. The rates of solved traffic crimes are typically low, compared to criminal crime rates. Traffic crimes per 10 000 people are overrepresented in the western (gorzowski – 78; zielonogórski ‒ 66), eastern (bialski ‒ 77) and central (sieradzki, skierniewicki) subregions of Poland, with the exception of the subregions which include large Polish cities (fig. 8). Basing on the crime patterns of the various categories of offences described above, the k-means cluster statistical technique has been used in the spatial typology analysis. Despite its popularity for general clustering, k-means suffers from major shortcoming: the number of clusters k has to be supplied by the user. In this paper a simple index for validating of the number of clusters has been used. It was the Davies-Bouldin Index (DBI). As it’s shown in fig. 9, the proper number of clusters is 4. As an example, consider partitions into 4 clusters of 66 Polish subregions (using police date crime) see the fig. 10. The different types include subregions: 1) the largest Polish cities (with highest criminal and commercial offences rates and the lowest rates of detectability); 2) located nearby the largest Polish cities (crime rates are similar to the Polish averages); 3) of North and West Poland (with highest criminal, traffic and commercial offences rates and high rates of detectability); 4) of Central and East Poland (with lowest criminal and commercial offences levels and highest rates of detectability).Celem tego opracowania jest przedstawienie zróżnicowania przestrzennego przestępczości na poziomie podregionów w Polsce. Pod uwagę wzięto główne rodzaje przestępstw: kryminalne, gospodarcze i drogowe. Ponieważ delikty te wykazują odmienne rozkłady przestrzenne postanowiono przedstawić typologię przestrzenną, dzięki której potwierdzono istniejące różnice natężenia zjawisk przestępczych między Polską wschodnią i zachodnią oraz niechlubnie wyróżniającą się pozycję dużych miast