## 2 Materials and Methods
### Evaluation: Platform, Data Sets, Methods, and Metrics  
All algorithms, which were examined in this research, were implemented at the Java Platform Standard Edition. Any external libraries and frameworks were not used. The above-mentioned methods of data particles creation were examined on two groups of imbalanced data sets. The first group consisted of 16 artificially generated data sets whose objects form the Moons and Circles shapes in the two-dimensional feature space. The data sets of this type can be generated by using the scikit-learn free library for Python [20]. However, the data sets used in this research were created by the self-implemented program in the Java language. The procedure of generating a class of data sets focuses on the combination of the circle equation with the conditional instructions. The information concerning the imbalance of individual data sets is presented in Table 1.  
The balanced variants of these data sets were presented in details in article [1], and at this time it was mentioned that these types of data sets have features that are problematic for classifiers based on centroids. Therefore, having the knowledge that the developed variant of geometrical divide is based on Centroid Based Classifier, its examination is important in terms of the inheritance of the mentioned feature. On the other hand, the second group of data sets was built based on real occupancy data set, which is available in the repository of the University of California in Irvine (UCI) [17]. There are three files in the directory downloaded from the mentioned source: one is a training data set and the two others are test data sets [21]. Due to the fact that in this study the k-fold cross validation method was used, those files were merged, and then based on that, the test and training sets were created. Taking into account that the discussed methods of creating data particles find application in the classification of two-dimensional data sets, it was possible to create 10 different two-dimensional sets based on the attributes offered by occupancy data set:  
* Temperature (\({}^{\circ}\)C),* Humidity/Relative humidity (%), which expresses the present state of absolute humidity in relation to the maximum humidity,
* Light (k),
* CO2 (ppm),
* Humidity Ratio/Absolute humidity (kgwater_vapor \(\times\) kgair\({}^{-1}\)), which expresses the present total mass of water vapor in relation to the volume or mass of air. Each data set consisted of 20,560 elements, where 4750 objects belonged to a positive class and the other 15,810 belonged to a negative class. The attributes applied therein are presented in Table 2, and before further processing the range of values for each attribute was mapped to the range [0, 1]. In the process of creating a predictive model, the purpose is to maximize its effectiveness. However, at the stage of its evaluation, particular attention should be paid to whether the model has not been overfitted in the design process. Symptoms of the occurrence of such a phenomenon are very good results on one specific data set and low efficiency at the moment of implementing such a classifier to another problem, in which a different data set is used [22]. The application of the k-fold cross validation method in the algorithm evaluation process prevents the aforesaid situation. It can be considered as a good practice, which is used in many field publications [23; 24]. The authors of this article, drawing on the experience of other researchers, also applied the above-mentioned method and parameterized it by setting the parameter k = 10.