## 4 Discussion
This difference stems from the different approaches used by the methods to assess feature relevance. By combining permutation importance and SHAP, we aimed to capture both global and local patterns in feature relevance. Indeed, unlike the permutation importance, which assesses model sensitivity by measuring the decrease in performance when a feature's values are randomly shuffled, SHAP extracts the Shapley values for each feature based on their contribution to the classifier prediction. In particular, different importance estimations from the two methods suggest that the feature contribution to the model's predictions may arise primarily through interactions with other features (which are captured by SHAP) rather than through a strong marginal effect on predictive accuracy when considered in isolation. An example is the step width in the _HC vs. rest_ task, which was not among the most important parameters for permutation importance but was relevant according to SHAP. Moreover, parameter inter-relationships are common for gait analysis data; thus, shuffling the values of a gait parameter can have a limited impact on the model output, since related information may be retrieved from another gait parameter. In Figure S5 of the Supplementary Materials, we investigated the relation between gait parameters, revealing a high correlation between the same parameters for left and right limbs and an inverse relationship between speed and double support phases, which is expected from a biomechanical perspective. On the contrary, SHAP can assign similar importance values when features are dependent. For instance, we observed that when stance and swing time were provided separately to the model, rather than the stance-to-swing ratio, they yielded comparable SHAP values. The results obtained in this work yielded lower classification performance than the ones obtained by [12], who used non-hierarchical clustering and presented accuracies spanning from 80% to 90% depending on the gait parameters employed. However, their study included a larger number of patients and parameters such as ankle ROM, which were excluded from our analysis for the reasons previously discussed. Studies such as [40] showed higher performance outcomes using different machine learning models (including Random Forest classifiers) by providing the classifiers with both the gait parameters and some anthropometric data, which in this case were not considered for classification. Indeed, we aimed to provide insights only on the gait parameters' role in the classification, using anthropometric data only for normalizing the parameters or for selecting the healthy controls within the same age range. Other studies applied ML techniques and explainability methods in gait analysis for neurodegenerative diseases. For instance, reference [41] used ground reaction forces to train a deep learning classifier for the recognition of [PERSON]'s disease and assessment of its severity. In particular, the model identifies specific frequency bands in the gait cycle associated with PD severity, which improves model interpretability. Similarly, reference [42] analyzed videos of patients to assess [PERSON]'s severity. In that work, SHAP and other methods were used to improve the interpretability of the results. Given the dataset employed, both these studies focused on spatial and temporal gait parameters. Many public gait analysis datasets, while valuable, present limitations for ML applications, which are mainly related to size and limited variability in participants. These limitations restrict the generalizability of models trained on such data. Additionally, differences in data acquisition protocols, sensor setups, and marker placements across datasets introduce biases that complicate cross-dataset comparisons and model transferability.