# A Selective Dynamic Sampling Back-Propagation Approach for Handling the Two-Class Imbalance Problem
## 5 Experimental Set-Up
### Parameter Specification for the Algorithms Employed in the Experimentation  
The stochastic back-propagation algorithm was used in this work (the source code of back-propagation algorithm and the approaches (dynamic sampling methods) and the datasets used in this work are available at Ref. [49]), and for each training process, the weights were ten times randomly initialized. The learning rate (\(\eta\)) was set to 0.1, and we established the stopping criterion at 500 epochs or if the MSE value is lower than 0.001. A single hidden layer was used. The number of neurons in the hidden layer was set to four for every experiment.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Dataset** & **\# of Features** & **\# of Minority Classes Samples** & **\# of Majority Class Samples** & **Imbalance Ratio** \\ \hline CAY0 & 4 & 838 & 5181 & 6.18 \\ CAY1 & 4 & 293 & 5726 & 19.54 \\ CAY2 & 4 & 624 & 5395 & 8.65 \\ CAY3 & 4 & 322 & 5697 & 17.69 \\ CAY4 & 4 & 133 & 5886 & 44.26 \\ CAY5 & 4 & 369 & 5650 & 15.31 \\ CAY6 & 4 & 324 & 5695 & 17.58 \\ CAY7 & 4 & 722 & 5297 & 7.34 \\ CAY8 & 4 & 789 & 5230 & 6.63 \\ CAY9 & 4 & 833 & 5186 & 6.23 \\ CAY10 & 4 & 772 & 5247 & 6.80 \\ FELT0 & 15 & 3531 & 7413 & 2.10 \\ FELT1 & 15 & 2441 & 8503 & 3.48 \\ FELT2 & 15 & 896 & 10,048 & 11.21 \\ FELT3 & 15 & 2295 & 8649 & 3.77 \\ FELT4 & 15 & 1781 & 9163 & 5.14 \\ SAT0 & 36 & 1508 & 4927 & 3.27 \\ SAT1 & 36 & 1533 & 4902 & 3.20 \\ SAT2 & 36 & 703 & 5732 & 8.15 \\ SAT3 & 36 & 1358 & 5077 & 3.74 \\ SAT4 & 36 & 626 & 5809 & 9.28 \\ SAT5 & 36 & 707 & 5728 & 8.10 \\ SEG0 & 19 & 330 & 1140 & 3.45 \\ SEG1 & 19 & 50 & 1420 & 28.40 \\ SEG2 & 19 & 330 & 1140 & 3.45 \\ SEG3 & 19 & 330 & 1140 & 3.45 \\ SEG4 & 19 & 50 & 1420 & 28.40 \\ SEG5 & 19 & 50 & 1420 & 28.40 \\ SEG6 & 19 & 330 & 1140 & 3.45 \\
92A0 & 38 & 190 & 4872 & 25.64 \\
92A1 & 38 & 117 & 4945 & 42.26 \\
92A2 & 38 & 1434 & 3628 & 2.53 \\
92A3 & 38 & 2468 & 2594 & 1.05 \\
92A4 & 38 & 747 & 4315 & 5.78 \\
92A5 & 38 & 106 & 4956 & 46.75 \\ \hline \end{tabular}
\end{table}
Table 1: A brief summary of the main characteristics of the new produced benchmarking dataset.  
All sampling methods (except ENN, SPIDER-1 and SPIDER-2, which employ three) use five nearest neighbors (if applicable) and sampling the training dataset to reach to relative class distribution balance (if applicable). ADASYN and ADOMS use the Euclidean distance, and the rest of the methods employ the Heterogeneous Value Difference Metric (HVDM) [50], if applicable. SPIDER-1 applies a weak amplification pre-processing option, and SPIDER-2 employs relabeling of noisy samples from the majority class and an amplification option. The sampling methods have been done using the KEEL [51].  
In order to identify the most suitable value for the variable \(\mu\), an independent validation set to avoid any bias in the performance on the testing data is considered, meaning that the testing data for this validation are not used (see Section 2.1). Thereafter, the most appropriate value for the variable \(\mu\) obtained for the datasets used in this work (Table 1) is 0.375. The results presented in this paper were obtained with \(\mu=0.375\). In addition, for this independent validation, only 200 epochs are used in the neural network training stage and about 8% of the samples of each dataset. This does not imply an important additional computational effort. The SDSAO and SDSAS methods are the proposed methods using ROS and SMOTE, respectively (see Section 4).