Spatial Relevance Reasoning

The requirements in section 5.1.4 show that a combination of neighborhood information and hierarchical information such as administrative units is useful. The definitions 5.8 and 5.9 allow a new type of reasoning: spatial relevance reasoning.

Spatial relevance reasoning is based on the assumption that the relative spatial relevance of two place names A and B is inversely proportional to

both their (spatial) distance in the connection graph, and their

(partonomic) distance in the decomposition tree. The easiest way to calculate a spatial relevance is to apply a linear function.

Definition 5.10

A spatial relevance is a cumulation of the distances and The weighting factor allows to bias the spatial relevance:

The weighting factor can be used to bias the computation either towards the evaluation of true spatial distance (i.e., an qualitative approximation of Euclidean distance), or distance within the partonomy (i.e., within a context- dependent hierarchy).

If place name structures use the same reference tessellation or frame of reference, the integration of multiple place name structures can easily be achieved.

Definition 5.11

Let be a place name with stands for query) with a spatial footprint consisting of a set of reference units that belongs to a standard

reference tessellation Then a distance field can

be computed in the connection graph based on the pSRT at granularity level L.

Based on the spatial distance of a place name that be-

longs to an arbitrary place name structure can be computed, provided its spatial footprint can be normalized to contain only reference units that are part of

Definition 5.12

The partonomic distances for all place names in are com- puted based on the partonomy encoded in Each node on the path to the top is assigned a partonomic distance of

For all nodes in the non-traversed sub-trees under P, is set to

Starting from the first common parent node of all place names

that share a minimal spatial distance to the hierarchical partonomy of is recursively traversed to the top node. Using this metric, we can compute the spatial relevance of any place name P that belongs to an ar- bitrary place name structure relative to a query location We will demonstrate the performance of spatial relevance reasoning in the following subsection.

5.4 Example

We will describe three different scenarios. Firstly, we will show that spatial relevance reasoning on the polygonal standard reference tessellation pSRT is possible. This means that the pSRT does not only serve as a de facto “common vocabulary”, Semantic Web users can also annotate their data with the help of these geographical terms. Secondly, we will show the reasoning capabilities with place name structures. Last, we demonstrate the integration capabilities between two or more place name structures.

Reasoning with Reference Units

Figure 5.9 shows an extraction of the map of landscapes of Germany. We see the fuzzy geographical area “Weserbergland” marked as light gray in figure 5.9a). The figure also shows those counties that are covered or partly cov- ered by the Weserbergland area (thick black lines). Figure 5.9b shows the partonomy of theses counties accordingly.

The BUSTER prototype (see also 7 on p. 125) follows the concept of spatial relevance reasoning as described above. Therefore, the user is able to determine whether they want to put emphasis on neighborhood or hierarchical information, by means of the weighting factor When choosing ‘neighbor- hood’ only and looking for a hotel in the county of Holzminden for example, a user would only get information items if they are annotated with the spatial term Holzminden. If we choose a wider radius, which is an additional feature for querying, we would also get those information items annotated with the direct neighbors of the county Holzminden. The following holds: the wider the radius the bigger the chance and higher the number of hits for a query. However, the spatial relevance equation 5.10 also makes sure that the possible answers are ranked higher the closer the information item is (to the spatial query).

Fig. 5.9. Landscapes of Germany.

If 50% neighborhood and 50% partonomic importance have been set with a radius set to 1, we get information items that are located in ‘Hameln-Pyrmont’ and ‘Schaumburg’. Figure 5.9b shows why: on the reference units level we can see that Holzminden, Hameln-Pyrmont, and Schaumburg are close together, being part-of Hannover. Since the radius is set to 1 both the neighborhood distance and the partonomic distance just cover those three counties. If we set the radius to 2, the next hierarchical level would be considered, which is the state of Niedersachsen in this case. This implies that the reasoner would also be able to find information items in ‘Braunschweig’, ‘Northeim’ and ‘Göttingen’ because they are part-of Niedersachsen.

If we would choose the hierarchical relevance only, the neighborhood in- formation is not considered. Suppose we are looking for an information item in the county of Göttingen (this could be the closest school for example). With a small radius of one or two we would get information items located in ‘Northeim’, ‘Holzminden’, ‘Schaumburg’, ‘Hameln-Pyrmont’ on the lowest level and ‘Braunschweig’ and ‘Niedersachsen’ on the next higher levels (fig. 5.9b). Please note that the direct neighbor ‘Kassel (Landkr.)’ is not consid- ered. Kassel (Landkr.) is part-of another state, namely the state of ‘Hessen’. Therefore, the hierarchical distance is much higher than the horizontal dis- tance. Thus, no answers to our query would be returned, which is correct as schools are tied to states.

Reasoning with Place Name Structures

For this application, we have chosen an area in the north-eastern part of Bavaria in Germany. In order to show the effect of our approach we first need

Fig. 5.10.Required for our example: (a) the spatial reference units as tessellation, (b) the place name regions, and (c) a combined schematic view of both.

a polygonal tessellation as spatial reference units. In our example, we have chosen the boundaries of the counties, however, this could also be any other polygonal tessellation (e.g., zip codes). As place name regions we have chosen a digital map of landscape areas. These areas are vague, i.e., even experts fight over the exact boundaries of these regions (e.g., Frankenwald (FW)). Figure 5.10 shows (a) the tessellation and (b) the polygons of the landscapes.

5.10(c) shows both layers combined in a schematic view for better under- standing. If we look for an accommodation in a certain area, e.g., the ‘Franken- wald’ our approach would map this place name region into discrete space (the reference units). This is done by the determination of the upper and lower approximation as described in [120]. Let’s say the approximation starts with an arbitrary polygon, e.g., the landscape polygon of the Frankenwald (FW).

Figure 5.11 a and b show both, the upper and the lower approximation of this polygon. The reasoner would now be able to derive the possible answers and rank them according to the users specifications. At the moment, the reasoner considers the upper approximation only, however, a more precise mapping is currently under development. The reasoner also finds information items that are annotated with the county names directly. Hence, the user is able to

Fig. 5.11. (a) Upper and (b) lower approximation for the place name region Frankenwald.

type in more common names such as widely knows landscapes (Frankenwald) rather than specify non-intuitive reference units. This shows the flexibility of our approach: the user can type in place names but the knowledge engineer who annotates the information items for the Semantic Web is able to use both place names and county names.

Mapping Between Two Place Name Structures

Another important, if not the most important, feature of our approach is the ability to compute the spatial relevance of any place name P that belongs to an arbitrary place name structure relative to a query location Figure 5.12 schematically shows the mapping between two place name structures. The spatial relevance of a place name P in (modeling natural regions

in Germany) with respect to a query location in (modeling the

distribution of the regional offices of a firm) is computed as function of the geographic location of P and its position within the hierarchical structure of This means that we would be able to find eligible information items anno- tated by different users using their own place name structure (regional offices of a company are a good example). However, this hold only if the Compre- hensive Source Description (see section 3) points to the same reference tessel- lation. This is analogue to the common vocabulary described in section 4.

Fig. 5.12. Two place name structures and their mapping onto the standard reference tessellation.