## 5 Discussion
### Workflow to Guide the Selection of a Decision-Map Technique  
After combining all the results of our evaluation, we can see that there was no clear winner among the studied decision-map techniques. When we considered the global quality metrics (Section 3.1), we found that each method reached its maximal quality on different datasets. Surprisingly, the unsupervised method (DBM) sometimes scored higher than the supervised ones (SDBM and DV) on the MNIST dataset. However, the DBM's failure on the Reuters dataset indicates that more challenging datasets may still require some level of supervision.  
Figure 12: Decision maps for different neural networks (see Section 5.1).  
The results of the local metrics provide more insights into our conclusion about there being no winner. For the synthetic dataset, all methods exhibited quite similar patterns, except for DV's poor smoothness and the SDBM's slightly worse class stability. For the real-world datasets, the patterns were less distinct. Yet, some trends can be discerned. The smoothness of DV was consistently low, regardless of the simplicity or complexity of the datasets. Additionally, DV and the SDBM consistently showed more representative distances (\(B\) and \(N\)) compared to the DBM.  
Concerning speed, the SDBM and SBM were clear winners--they definitely surpassed DV in both training and inference (map construction) times by up to three orders of magnitude, which makes the latter unsuitable for creating decision maps in real-world application scenarios, especially when using more time-consuming classifiers such as SVM.  
Compared to the SDBM and DV, the DBM has a separate advantage. As outlined in Section 2, the DBM allows one to use any chosen direct projection function \(P\) to create decision maps. This can be important in cases where one knows that a given \(P\) is optimal, either for quantitative reasons or because it creates projections that are easier to interpret by users.  
In conclusion, since there was no clear winner, the choice of a decision-map method should be guided by the specific requirements and constraints of individual use cases. We encapsulate this by proposing a workflow for choosing a method to create decision maps, as illustrated in Figure 13. Given a specific dataset and a set of potential classifier candidates, the workflow can assist users in making a choice by following the steps below:  
1. If the user has already chosen a projection function \(P\), they should select the DBM, as this is the only method that can accommodate a predefined \(P\), and proceed to step 4.
2. If the user does not have a specific \(P\), the next key aspect to consider is computational efficiency. If speed is important and the data to be visualized are large, DV should be excluded from consideration, and the workflow proceeds to step 4.
3. If the user does not have a specific \(P\) and computational efficiency is not a concern, one should consider if smoothness is important. If yes, DV should be excluded, and one can proceed to step 4.
4. If more than a single classifier-decision map combination remains to be chosen from, global quality metrics can be used to select the optimal one. The key metrics to use here are \(ACC_{C}\), \(ACC_{M}\), and \(Cons_{d}\) (defined in Section 3.1), which can be computed for any combination of direct projection, inverse projection, and classifier. Note that \(Cons_{p}\) and \(\tilde{S}\) are not available when the selected projection \(P\) cannot infer new data, such as in the case of non-parametric, non-out-of-sample projections like t-SNE.
5. Finally, visualizations of local metrics can be used to gain more trust in and/or a better understanding of the behavior of the chosen decision map, as described in the scenarios in Section 4.