# A Geo-Clustering Approach for the Detection of Areas-of-Interest and Their Underlying Semantics +
## 4 Experiments and Results
### Experimental Evaluation
#### 4.2.1 Quantitative Results  
In order to assess the quality of the produced geo-clusters, i.e., evaluate their size, popularity and number of touristic POIs that they contain, we perform a quantitative evaluation of the proposed geo-clustering algorithm using the following metrics, each evaluated on a set of extracted geo-clusters \(C_{p}\) for a given run of the algorithm with \(p\) denoting the selected input parameters:  
* _Avg. POIs per Geo-Cluster (APOIpGC)_ is the mean value of the number of POIs that are located within the \(n\) tiles that comprise a geo-cluster \(C_{i}\in C_{p}\). This metric may be regarded as the \"touristic value\" of the geo-cluster and may be calculated as: \[APOIpGC(C_{p})=\frac{1}{n}\sum_{j=1}^{n}|\text{POI}_{j}|,\] (3) where POI\({}_{j}\) denotes the set of POIs for a given tile of \(C_{i,p}\) and \(|\bullet|\) denotes set cardinality.
* _Avg. Visitors per Geo-Cluster (AVpGC)_ is the average number of visitors for a geo-cluster \(C_{i,p}\) and may be calculated as: \[AVpGC(C_{p})=\frac{1}{n}\sum_{j=1}^{n}|\text{V}_{i}|,\] (4) where V\({}_{i}\) denotes the set of unique visitors, for a given tile of \(C_{i,p}\).
* _Avg. Photos per Geo-Cluster (APpGC)_ is the mean value of the number of geo-tagged photos within a geo-cluster and may be calculated as \[APpGC(C_{p})=\frac{1}{n}\sum_{j=1}^{n}|\text{P}_{i}|,\] (5) where P\({}_{i}\) denotes the set of geo-tagged photos, for a given tile of \(C_{i,p}\).
* _Avg. Geo-Cluster Size (AGCS)_ is the average area of a geo-cluster, in Km\({}^{2}\): \[AGCS(C_{p})=\frac{1}{n}\sum_{i=1}^{n}\text{area}(C_{i,p}),\] (6)  
Figure 3: Density-based visualizations regarding the distribution of geo-tagged photos (**a**) and POIs (**b**) in the broader region of Attica and the centre of Athens.  
* _Avg. Tiles per Geo-Cluster (ATpGC)_. The mean value of the number of tiles that form a geo-cluster. \[ATpGC(C_{p})=\frac{1}{n}\sum_{i=1}^{n}|T_{i}|,\] (7) where \(T_{j}\) denotes a the set of tiles that comprise a given geo-cluster \(C_{i,p}\) and \(n\) is the number of produced geo-clusters.  
In total, we performed 36 experiments, however we opted to present a subset of them, so as to facilitate both the reader and the qualitative evaluation process, presented in Section 4.2.2 and ruled out those that produced either a large number of relatively small AOIs (e.g., consisting of 1-2 tiles) or a small number of relatively large AOIs (e.g., less than 5 AOIs in total). The selected cases along with  
Figure 4: Geo-clusters produced within the selected urban area, i.e., the center of the city of Athens for several parameters of the proposed algorithm. Each geo-cluster has been randomly colored. Initial tile boundaries are overlaid. Tiles colored with white did not initially contain any photo, thus were excluded from the algorithm.  
the results of the proposed algorithm are summarized in Figure 4. Results using the aforementioned metrics are summarized in Table 2. By careful observation of this table, we may come to the following conclusions: Lower tile sizes (i.e., \(W_{R}=50,100\) m) in general lead to more smaller clusters with smaller number of contained POIs, visitors and consequently photos. On the contrary, by increasing tile size (i.e., setting \(W_{R}=200\) m), allows clusters to become more cohesive. As it will be presented in next Section 4.2.2, this is a feature appreciated by real-life users.