## 4 Discussion  
A new variant of the geometrical divide approach called the Unequal Geometrical Divide (UGD) was proposed in this article. It is the modification of the existing Geometrical Divide (GD) method. The conducted experiments showed that in the classification of imbalanced data sets the feature of the Geometrical Divide approach is the improvement of recall value in relation to the method creating data particle based on class by a compound of \(1\div 1\) cardinality (1 CT1P). The GD outperforms UGD on the Moons and Circles data sets, in which atomic data particles do not overlap in the feature space. On the other hand, on the data sets whose elements overlap in the feature space, better results are obtained by the Unequal Geometrical Divide algorithm. This research showed that the UGD method allows to improve precision value in relation to the 1 CT1P method. However, the second experiment reported that in the problem of occupancy detection the UGD strives to the balanced improvement of the precision and recall. Based on the above-mentioned observations it can be stated that in the occupancy detection problem, which for instance will be oriented on the chasing of intrusions, the Geometrical Divide will be a better choice, because in this problem the correct prediction of a small number of samples constituting a minority class will be the most important. On the other hand, the Unequal Geometrical Divide will be a better choice in the occupancy detection problem oriented on the overall monitoring, in which the correct information if the room is occupied or unoccupied are equally important,  
The second experiment showed as well that the best results were obtained on the following data sets: \begin{table}
\begin{tabular}{c c c c} \hline
**Data Set** & **1 CT1P** & **GD** & **UGD** \\ \hline occupancy\_12 & 0.120 & 0.179 & 0.013 \\ occupancy\_13 & 0.118 & 0.077 & 0.071 \\ occupancy\_14 & 0.075 & 0.200 & 0.018 \\ occupancy\_15 & 0.230 & 0.207 & 0.001 \\ occupancy\_23 & 0.091 & 0.100 & 0.072 \\ occupancy\_24 & 0.050 & 0.211 & 0.034 \\ occupancy\_25 & 0.199 & 0.200 & 0.010 \\ occupancy\_34 & 0.122 & 0.104 & 0.077 \\ occupancy\_35 & 0.080 & 0.099 & 0.090 \\ occupancy\_45 & 0.022 & 0.158 & 0.041 \\ \hline \end{tabular}
\end{table} 
Table 8: The absolute values of difference between precision and recall obtained by the 1 CT1P, GD and UGD methods on individual data sets concerning occupancy detection. \begin{table}
\begin{tabular}{c c c} \hline
**Comparison** & **Adjusted \(p\)-Value** & **Statistically Significant Difference** \\ \hline UGD vs. GD & 0.00022 & YES \\ UGD vs. 1 CT1P & 0.02950 & YES \\ GD vs. 1 CT1P & 0.12751 & NO \\ \hline \end{tabular}
\end{table} 
Table 9: Results of conducted statistical test. * occupancy_13,
* occupancy_23,
* occupancy_34,
* occupancy_35. Referring to Table 2, it can be stated that each of the above-listed data sets based on the attribute storing the value from light measurement. Therefore, it can be concluded that the light value is the most relevant in the process of occupancy detection. The obtained results showed that the geometrical divide approaches (GD and UGD) improves the results obtained by the 1 CT1P method in the classification process of imbalanced data sets, in which a linear decision boundary does not exist, the centroids are close to each other and objects belonging to various classes overlap in a feature space. Through the obtained results, it was demonstrated that the methods of data particles creation by their geometrical divide outperform the approach of creating data particle based on class by a compound of \(1\div 1\) cardinality in the occupancy detection problem. The disadvantage of the existing data particle geometrical divide approaches is a necessity of the manual selection of the target data particles number to be achieved as a result of their divide. The problem is exacerbated by the fact demonstrated in both experiments, as the mentioned number is usually different for each of the analysed data sets.