# 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{3-7}  & & & \multicolumn{2}{c}{**Label Distribution**} & \multicolumn{2}{c}{**Label Pair Distribution**} \\ \cline{4-7}  & & & **Unconstrained** & **Constrained** & **Unconstrained** & **Constrained** \\ \hline
**emotions** & \(2.64\times 10^{-2}\) & \(6.61\times 10^{-3}\) & \(1.54\times 10^{-2}\) & \(1.93\times 10^{-2}\) & \(\mathbf{4.81\times 10^{-3}}\) & \(\mathbf{4.63\times 10^{-3}}\) \\ \hline
**scene** & \(1.08\times 10^{-1}\) & \(2.83\times 10^{-2}\) & \(7.84\times 10^{-2}\) & \(8.11\times 10^{-2}\) & \(\mathbf{1.97\times 10^{-2}}\) & \(\mathbf{2.11\times 10^{-2}}\) \\ \hline
**genbase** & \(1.98\times 10^{-2}\) & \(1.73\times 10^{-2}\) & \(\mathbf{1.71\times 10^{-2}}\) & \(1.74\times 10^{-2}\) & \(\mathbf{1.37\times 10^{-2}}\) & \(\mathbf{1.37\times 10^{-2}}\) \\ \hline
**medical** & \(1.61\times 10^{-2}\) & \(1.28\times 10^{-2}\) & \(1.53\times 10^{-2}\) & \(1.46\times 10^{-2}\) & \(\mathbf{1.17\times 10^{-2}}\) & \(\mathbf{1.17\times 10^{-2}}\) \\ \hline
**yeast** & \(1.57\times 10^{-3}\) & \(6.45\times 10^{-4}\) & \(8.39\times 10^{-4}\) & \(8.81\times 10^{-4}\) & \(\mathbf{3.60\times 10^{-4}}\) & \(\mathbf{3.35\times 10^{-4}}\) \\ \hline
**enron** & \(6.68\times 10^{-4}\) & \(5.61\times 10^{-4}\) & \(5.66\times 10^{-4}\) & \(\mathbf{5.57\times 10^{-4}}\) & \(\mathbf{4.16\times 10^{-4}}\) & \(\mathbf{4.19\times 10^{-4}}\) \\ \hline
**rcv1 subset4** & \(3.35\times 10^{-4}\) & \(2.10\times 10^{-4}\) & \(2.63\times 10^{-4}\) & \(2.54\times 10^{-4}\) & \(\mathbf{1.87\times 10^{-4}}\) & \(\mathbf{1.86\times 10^{-4}}\) \\ \hline
**rcv1 subset5** & \(2.98\times 10^{-4}\) & \(2.29\times 10^{-4}\) & \(2.40\times 10^{-4}\) & \(2.41\times 10^{-4}\) & \(\mathbf{1.73\times 10^{-4}}\) & \(\mathbf{1.72\times 10^{-4}}\) \\ \hline
**rcv1 subset5** & \(2.85\times 10^{-4}\) & \(1.96\times 10^{-4}\) & \(2.34\times 10^{-4}\) & \(2.30\times 10^{-4}\) & \(\mathbf{1.69\times 10^{-4}}\) & \(\mathbf{1.69\times 10^{-4}}\) \\ \hline
**rcv1 subset5** & \(2.92\times 10^{-4}\) & \(1.85\times 10^{-4}\) & \(2.40\times 10^{-4}\) & \(2.38\times 10^{-4}\) & \(\mathbf{1.73\times 10^{-4}}\) & \(\mathbf{1.70\times 10^{-4}}\) \\ \hline
**rcv1 subset1** & \(2.70\times 10^{-4}\) & \(1.78\times 10^{-4}\) & \(2.11\times 10^{-4}\) & \(2.05\times 10^{-4}\) & \(\mathbf{1.51\times 10^{-4}}\) & \(\mathbf{1.52\times 10^{-4}}\) \\ \hline
**tmc2007\_500** & \(4.69\times 10^{-4}\) & \(1.94\times 10^{-4}\) & \(3.82\times 10^{-4}\) & \(3.71\times 10^{-4}\) & \(\mathbf{1.30\times 10^{-4}}\) & \(\mathbf{1.18\times 10^{-4}}\) \\ \hline
**bibtex** & \(1.96\times 10^{-4}\) & \(1.68\times 10^{-4}\) & \(1.82\times 10^{-4}\) & \(1.80\times 10^{-4}\) & \(\mathbf{1.44\times 10^{-4}}\) & \(\mathbf{1.45\times 10^{-4}}\) \\ \hline
**Corel5k** & \(1.72\times 10^{-4}\) & \(1.43\times 10^{-4}\) & \(1.59\times 10^{-4}\) & \(1.59\times 10^{-4}\) & \(\mathbf{1.29\times 10^{-4}}\) & \(\mathbf{1.29\times 10^{-4}}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Label Pair Distribution of different splitting algorithms. In bold the results that are better than the stratification method. In all cases, the evolutionary algorithm that uses _LPD_ as fitness function obtains the best results. This does not happen when the _LD_ is used as fitness function.