# EvoSplit: An Evolutionary Approach to Split a Multi-Label Data Set into Disjoint Subsets
## 3 First Approach: Single-Objective Evolutionary Algorithm
### Results
\begin{table}
\begin{tabular}{l c c c c c c} \hline \hline  & \multirow{2}{*}{**Random**} & \multirow{2}{*}{**Stratification**} & \multicolumn{6}{c}{**Evolutionary Algorithm**} \\ \cline{4-7}  & & & **Label Distribution** & **Label Pair Distribution** \\ \cline{4-7}  & & & **Unconstrained** & **Constrained** & **Unconstrained** & **Constrained** \\ \hline
**emotions** & \(3.77\times 10^{-2}\) & \(6.45\times 10^{-3}\) & \(\mathbf{2.87\times 10^{-3}}\) & \(\mathbf{2.85\times 10^{-3}}\) & \(1.84\times 10^{-2}\) & \(1.79\times 10^{-2}\) \\ \hline
**scene** & \(2.68\times 10^{-2}\) & \(1.69\times 10^{-3}\) & \(\mathbf{1.27\times 10^{-3}}\) & \(\mathbf{1.42\times 10^{-3}}\) & \(2.46\times 10^{-2}\) & \(2.38\times 10^{-2}\) \\ \hline
**genbase** & \(1.38\times 10^{-2}\) & \(4.75\times 10^{-3}\) & \(\mathbf{4.54\times 10^{-3}}\) & \(\mathbf{4.48\times 10^{-3}}\) & \(1.03\times 10^{-2}\) & \(1.30\times 10^{-2}\) \\ \hline
**medical** & \(7.68\times 10^{-3}\) & \(2.96\times 10^{-3}\) & \(\mathbf{2.88\times 10^{-3}}\) & \(\mathbf{2.79\times 10^{-3}}\) & \(7.56\times 10^{-3}\) & \(7.61\times 10^{-3}\) \\ \hline
**peast** & \(5.72\times 10^{-3}\) & \(1.47\times 10^{-3}\) & \(\mathbf{5.24\times 10^{-4}}\) & \(\mathbf{5.12\times 10^{-4}}\) & \(\mathbf{1.35\times 10^{-3}}\) & \(\mathbf{1.29\times 10^{-3}}\) \\ \hline
**enron** & \(2.89\times 10^{-3}\) & \(1.79\times 10^{-3}\) & \(\mathbf{8.90\times 10^{-4}}\) & \(\mathbf{8.34\times 10^{-4}}\) & \(\mathbf{1.46\times 10^{-3}}\) & \(\mathbf{1.45\times 10^{-3}}\) \\ \hline
**rcv1 subset4** & \(1.55\times 10^{-3}\) & \(4.24\times 10^{-4}\) & \(\mathbf{3.72\times 10^{-4}}\) & \(\mathbf{3.30\times 10^{-4}}\) & \(5.87\times 10^{-4}\) & \(5.73\times 10^{-4}\) \\ \hline
**rcv1 subset5** & \(1.60\times 10^{-3}\) & \(4.96\times 10^{-4}\) & \(\mathbf{3.42\times 10^{-4}}\) & \begin{table}
\begin{tabular}{c c c} \hline \hline  & \multicolumn{2}{c}{**All Cases**} \\ \hline  & **emotions** & 0 \\ \hline  & **scene** & 0 \\ \hline  & **genbase** & 10 \\ \hline  & **medical** & 10 \\ \hline  & **yeast** & 0 \\ \hline  & **enron** & 10 \\ \hline  & **rcv1 subset4** & 10 \\ \hline  & **rcv1 subset3** & 10 \\ \hline  & **rcv1 subset5** & 10 \\ \hline  & **rcv1 subset5** & 10 \\ \hline  & **rcv1 subset2** & 10 \\ \hline  & **rcv1 subset2** & 10 \\ \hline  & **rcv1 subset1** & 10 \\ \hline  & **tmc2007\_500** & 0 \\ \hline  & **bibtex** & 0 \\ \hline  & **tmc2007\_500** & 0 \\ \hline  & **bibtex** & 0 \\ \hline  & **Corel5k** & 10 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Number of folds that contain at least one label with zero positive examples (\(FZ\)). All the splitting algorithms obtain the same results. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Random** & **Stratification** & **All EAs** \\ \hline
**emotions** & 0 & 1.2 & 0 \\ \hline
**scene** & 0 & 1.4 & 0 \\ \hline
**genbase** & 0 & 0.8 & 0 \\ \hline
**medical** & 0 & 1.2 & 0 \\ \hline
**yeast** & 0 & 4.2 & 0 \\ \hline
**enron** & 0 & 3.8 & 0 \\ \hline
**rcv1 subset4** & 0 & 3.8 & 0 \\ \hline
**rcv1 subset3** & 0 & 4.8 & 0 \\ \hline
**rcv1 subset5** & 0 & 6.6 & 0 \\ \hline
**rcv1 subset2** & 0 & 3.6 & 0 \\ \hline
**rcv1 subset1** & 0 & 7.2 & 0 \\ \hline
**tmc2007\_500** & 0 & 19.8 & 0 \\ \hline
**bibtex** & 0 & 14 & 0 \\ \hline
**Corel5k** & 0 & 6.2 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Examples Distribution of different splitting algorithms. Only the stratification method deviates from zero. Tables 3 and 4 show that the evolutionary approach gets better results than Stratification only for the metric that is employed as fitness function. There are only some few cases in which good results are obtained for both metrics, the Label Distribution and the Label Pair Distribution simultaneously. On the other hand, the Stratification method obtains splits that behave well for both metrics, even if the best results for each metric are obtained with the evolutionary approaches.