The usefulness of such a programme soon becomes obvious. "Take, for instance, the commissioner of London's police force, who has to allocate the patrols at the beginning of February in an effort to reduce crime to a minimum. To assist him in his task, he uses a database that lists all the past offences. He can relatively quickly obtain a map of London that shows the spatial distribution of crime for the month of January and base himself on the assumption that the distribution will be similar in February." But there’s a slight problem for the head of Scotland Yard. In 2012, approximately 1.2 million offences were listed for London alone, which makes almost 100,000 for the month of January. "A simple spatial distribution of the crimes committed, where every offence is represented by a dot on a map, is illegible."

Hence, SOLAP allow you to gather and summarise these values according to what it is you want to know. "On a vectorial level, I reoganised these offences by aggregating them on an entity basis, which, in this case, represents the different police sectors in London. The colour of these polygons varies according to the number of dots they contain. This gives you a denstiy of offences aggretated in a discretized space." But this vector map only serves to illustrate the use of SOLAP in general. Because Jean-Paul Kasprzyk wasn’t interested in the vector mode, but sought to integrate a continuous space in this type of model, using the raster method.

From vector to raster for spatial continuity

"The main problem with vectorial mapping techniques", the geomatics specialist points out, "is that they bias the values you’re trying to define. For instance, the purpose of this list of break-ins is to locate hotspots; i.e., places with a higher concentration of crime. An analysis that will then allow the user to decide where best to deploy the police patrols, and therefore better prevent crime. However, vector maps have a geometrically frozen discrete space, following a random decision, in this case, the distinction of the police sectors." Therefore, the form of the hotspots shown on the map are influenced by these borders, whose outline is independent of the crimes. Consequently, areas with a low crime rate can be part of a section with a high concentration of crime, and appear on the map as hotspots, and vice versa. Hence the aim to integrate a continuous space in the model.

Police services are already favouring this type of more accurate map. For this purpose, they use a particular algorithm, KDE (Kernal Density Estimation). "Initially, the offences are represented by a cloud of points. These points are discrete values. To integrate them into a continuous space, you have to smooth them, which is what this algorithm does. More precisely, it sweeps a territory and in every pixel of a raster, it generates a relative value that depends on the number of crimes over a given time, and their proximity in relation to the pixel." Ultimately, the algorithm gives each pixel a colorimetric variation according to the density of crime. The data is aggregated at pixel level and no longer depends on artificial borders, but on their actual location.  The map can be more or less precise, according to the resolution of the pixels, but also the smoothing window. "The bigger this windrow, the smoother the surface will be over a large distance. Therefore, there will be few hotspots, which will be quite big. The information is less precise but this can be useful if you want to identify the main risky areas of the city (global analysis). On the other hand, the smaller the window, the more precise the resolution will be, and a lot of small hotspots will appear. The map will be very precise, but the data will be spatially less aggregated (local anlaysis)." Hence, there is a whole series of parameters that have an impact on the visual aspect of the map. The important thing here, as in many fields, is to find a happy medium to obtain a useful image.