# EvoSplit: An Evolutionary Approach to Split a Multi-Label Data Set into Disjoint Subsets
## 7 Conclusions  
This paper presents EvoSplit, a novel evolutionary method to split a multi-label data set into disjoint subsets. Different proposals, single-objective and multi-objective, using diverse measures as fitness function, have been proposed. A constraint has also been introduced in order to ensure that, if possible, labels are distributed among all subsets. In almost all the cases, the multi-objective proposal obtains state-of-the-art results, improving or matching the quality of the splits officially provided or obtained with iterative stratification methods. The improvement of EvoSplit over previous methods is highlighted when applied to very large data sets, as those currently used in machine learning and computer vision applications. Moreover, the introduction of the constrained optimization decreases the chance of producing subsets with zero positive examples for one or more labels. This should have an effect on the training as there will be fewer labels for which there are no training or validation examples. A very relevant result is that EvoSplit is able to find splits that fulfill the constrain without affecting too much the distribution of labels and label pairs. EvoSplit is able to obtain better distributions of the original data sets considering the desired size of the subsets as a hard constraint, i.e., ensuring that the Examples Distribution is equal to zero. This is not the case for the iterative stratification method. The subsets obtained with EvoSplit allow better classification results and reduce the variance in the performance across subsets/folds. Only in the case of the Imagenet data set, the best results are not obtained by the multi-objective EA but by the single-objective EA optimizing the Label Pair Distribution measure. An explanation to this might be related to the relation in the diversity between labels and pair labels for this data set. This data set has a particular characteristic: there are \begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline  & \multirow{2}{*}{**Official**} & \multirow{2}{*}{**Random**} & \multicolumn{6}{c}{**Evolutionary Algorithm**} & \multicolumn{2}{c}{**MOEA**} \\ \cline{4-9}  & & & **Label Distribution** & & **Label Pair Distribution** & & \\ \cline{3-9}  & & & **Unconst.** & **Const.** & **Unconst.** & **Const.** & **Unconst.** & **Const.** \\ \hline
**LD** & \(2.04\times 10^{-6}\) & \(2.86\times 10^{-6}\) & \(1.33\times 10^{-6}\) & \(1.35\times 10^{-6}\) & \(9.17\times 10^{-7}\) & \(8.02\times 10^{-7}\) & \(1.04\times 10^{-6}\) & \(1.48\times 10^{-6}\) \\ \hline
**LPD** & \(4.21\times 10^{-7}\) & \(6.45\times 10^{-7}\) & \(3.34\times 10^{-7}\) & \(3.36\times 10^{-7}\) & \(2.23\times 10^{-7}\) & \(1.94\times 10^{-7}\) & \(2.58\times 10^{-7}\) & \(3.49\times 10^{-7}\) \\ \hline
**FZ** & \(1\) & \(1\) & \(1\) & \(1\) & \(1\) & \(1\) & \(1\) \\ \hline
**FLZ** & \(361\) & \(495\) & \(466\) & \(36\) & \(415\) & \(36\) & \(429\) & \(19\) \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Evaluation of the different splitting approaches of the Imagenet subset in the Tencent ML-Images database. In bold the results that are better than the official method, usually employed in the literature. NOTE: The results for the Stratification method are not shown as no result was obtained after 10 days of processing. Therefore, \(ED\) is not shown as it only deviates from zero for that method.