## 3 Results  
This section presents the performance of the classifiers employed in the different classification tasks, followed by the results of the importance of the gait parameters. As discussed in Section 2.2, we extracted the performance evaluation metrics for every cross-validation fold. The results shown from now on have been averaged over the folds, and the standard deviation of the metrics is also shown to give insights on the fluctuation of the values.  
By using only the gait parameters as input, the classifiers achieved optimal performance in distinguishing healthy subjects from people affected by a specific neurodegenerative disease, particularly in the case of Parkinson's disease (PD) and hereditary spastic paraplegia (HSP), as shown in Figure 2.  
To avoid age-related classification bias, the classifiers were trained using a population of healthy controls matched in age with the diseased groups. This was particularly important in the _HC vs. PD_ task, where the average age of participants with [PERSON]'s disease was notably higher than that of the healthy controls.  
As expected, the binary classification tasks outperformed the multi-class setting across all classifiers. In the multi-class case, the accuracy results ranged from \(59\pm 9\%\) for the MLP to \(65\pm 6\%\) for the XGB. Similar trends were observed across the other evaluation metrics. The binary classification tasks reached accuracy values up to \(85\%\), particularly in the ones when only one disease was considered. Indeed this was expected, as each disease is characterized by specific gait alterations. In contrast, grouping all diseases into a broader class (i.e., in the _HC vs. rest_ task) reduced discriminability, which was likely due to overlapping gait features among the conditions. Consequently, the relative importance of gait parameters is expected to vary depending on the disease considered.  
In this regard, XAI methods were used here to enhance the model interpretability by identifying the most influential gait parameters in classification. Figure 3 shows the permutation importance for all the classifiers in different classification tasks.  
As can be seen, many parameters had importance values within \(\pm\)0.05, with standard deviations that made the values consistent with zero, meaning that the importance of these gait parameters was not statistically significant. However, the walk ratio and knee ROM emerged as the most important gait parameters for all the classifiers. Figure 4 depicts the importance of the gait parameters estimated with the SHAP explainability method. In line with the permutation importance results, walk ratio and knee ROM were among the most relevant gait parameters, together with step width, which was significantly important for every classifier in the _HC vs. CA_ classification task.  
Figure 2: Performance scores (i.e., accuracy, precision, recall, fl-score, and AUC metrics) from every classifier in each classification task. The scores are averaged over the folds and evaluated on the test set. The error bars represent the standard deviation of the metric values obtained from every fold.  
Figure 3: Permutation importance of every gait parameter for every classifier and classification task. The values are collected for every fold so that the bin height is the average, and the black vertical bars is the standard deviation of the permutation importance over the folds. Higher values of the score indicate higher relevance of the feature analyzed.