## 3 Results  
The research was divided into two experiments. The imbalanced data sets with different characteristic were applied in each of them. The mentioned experiments revolve around the comparison of results expressed by precision, recall, and F-measure and were obtained by the methods of data particles creation listed below:  
* the method of creating the data particles based on classes by compound of \(1\div 1\) cardinality (ICT1P) [3];
* the Geometrical Divide (GD) approach, creating new data particles by an equal divide of all existing data particles [1];
* the Unequal Geometrical Divide (UGD) algorithm creating data particles by divide of only the biggest data particle within the current iteration.  
Each of the mentioned methods was combined with the standard Centroid Based Classifier (CBC) and with three algorithms of data particle mass determination:  
* n-Mass Model (n-MM) [19], which determines the value of data particles masses based on a size of classes;
* Stochastic Learning Algorithm (SLA) [18], in which: \(\bigcirc\) maximum number of iterations maxIters = 50; \(\bigcirc\) coefficient of the mass value update \(\xi\) = 0.0001; \(\bigcirc\) expected error threshold \(\varepsilon\) = 0.00;
* Batch-update Algorithm [18], in which the coefficient of the mass value update \(\xi\) = 0.0001.  
As a result, 12 hybrid approaches combining each of the data particle creating methods with each algorithm of the data particle mass determination and with Centroid Based Classifier were implemented:  
* 1 CT1P-SLA,
* 1 CT1P-n-MM,
* 1 CT1P-CBC,
* GD-SLA,
* GD-BLA,
* GD-n-MM,
* GD-CBC,
* UGD-SLA,
* UGD-BLA,
* UGD-n-MM,
* UGD-CBC.  
Therefore, for a single data set, 12 values of precision, recall and F-measure were obtained, which were classified into 3 groups, in the criterion of applied data particle creation algorithm:  
* 1 CT1P,
* GD,
* UGD.  
Each group consisted of four precision, recall, and F-measure values referring to results obtained by one of the mentioned approaches, which was combined with three algorithms of data particle mass determination and Centroid Based Classifier. Each of the three groups was pre-processed, by rejecting the maximum and minimum values, then the arithmetic mean for one group was calculated based on the results of the two others. In this way, a single precision, recall, and F-measure value was obtained for each method of data particle creation. These acquired results constituted the object for further analysis.  
As a result of applying k-fold cross validation, each data set was divided in accordance with the pseudocode presented in Algorithm 1.  
```
1:\(D\leftarrow\{\epsilon_{0},\ldots,\epsilon_{n}\}\)//set of data set elements
2:\(V\leftarrow\emptyset\)//set of validation data set elements
3:\(T\leftarrow\emptyset\)//set of training data set elements
4:\(I\leftarrow\emptyset\)//set of cross validation iterations; single iteration is element consisting of \(V\) and \(T\)
5:\(k\gets 10\)
6:for\(i\gets 0\)to\(k-1\)do
7:\(begin\gets i^{*}n/k\)
8:end\(\gets begin\_idx+n/k-1\)
9:for\(i\gets 0\)to\(n\)do
10:if\(j\succ=begin\_idx\)and\(j\prec=end\_idx\)then
11:\(V\gets V\cup D_{j}\)
12:else
13:\(T\gets T\cup D_{j}\)
14:endif
15:endfor
16:\(I\gets I\cup new\)Iteration(\(V,T\))
17:\(V\leftarrow\emptyset\)
18:\(T\leftarrow\emptyset\)
19:endfor
```  
**Algorithm 1** k-Fold Cross Validation.