## 4 Discussion  
Neurodegenerative diseases exhibit distinct gait characteristics, as revealed by the explainability methods used in this study. Compared to healthy gait, cerebellar ataxia shows reduced step and stride length, swing time, speed, and cadence and increased step width, stance time, and double support time. Moreover, many of these parameters show significant variability across different gait cycles [31]. This is consistent with our analysis: step width emerged as the most relevant gait parameter by SHAP for all the classifiers used, along with walk ratio, which is expected to decrease in atax gait due to reduced cadence and step length. For [PERSON]'s disease, the most important gait parameters for the classification, according to the explainability methods used, are the knee and hip ROMs and walk ratio. Indeed, as reported in [32; 33; 34], reduced ranges of motion are common gait impairments for  
Figure 4: Normalized SHAP importance of every gait parameter for every classifier and binary classification task. The bins represent the absolute SHAP values averaged over the folds, and the black vertical lines represent their standard deviation. Higher values of the score indicate higher relevance of the feature analyzed. Please note the different extent of the ordinate for the XGBoost classifier. PD patients, as well as an increased cadence and decreased step length, resulting in a lower walk ratio compared to healthy subjects. In the classification of hereditary spastic paraplegia (HSP), both SHAP and permutation importance highlighted the knee ROM and the stance-to-swing time ratio as key features, and these are consistent with known gait impairments in HSP [35]. Ankle ROM, although known to decrease in pathological gait [35; 36; 37; 38], was not used in our analysis. This decision was based on a systematic asymmetry observed in the left-limb data of healthy controls, which may have resulted in bias outcomes in our analysis. Further details are provided in Appendix A. In general, we can notice that some gait characteristics, such as reduced ROM in lower-limb joints, are similar among different diseases. This effect may explain the lower performance on the multi-class classification task. To provide more insights into the multi-class classification task and the classification errors for each class, we also computed the confusion matrices for every classifier, which are shown in Figure A4, and their results are discussed in Appendix C. It can be noticed that the greater source of confusion is related to misclassification of subjects affected by a disease, which were classified as healthy (which was the class with more subjects), and to misclassification between HSP and PD subjects. Other methods have been adopted to improve the performance for this task, including a hierarchical approach, which classifies first healthy subjects from subjects affected by any disease, with a second classifier dedicated to the classification of the specific disease. Additionally, oversampling techniques such as SMOTE [39] have been adopted to achieve class balance during training. However, the results obtained were compatible with the ones achieved through the classification approach described in Sections 2.2 and 2.3. More details on these methods can be found in Figures S3 and S4 in Supplementary Materials. The classification error between PD and HSP can be due to the overlap of gait parameters such as knee ROM (see Figure A1), which are considered relevant for classification and, at the same time, show a similar behavior between PD and HSP patients. In this regard, an in-depth analysis of the gait profiles may be beneficial for better distinguishing between different diseases. Moreover, a dataset with several gait cycles for each subject could also enable the evaluation of the relevance of the variability in certain gait parameters in different diseases. As illustrated in Figures 3 and 4, the features show different importance values, and gait parameters relevant for an XAI method cannot be as relevant for the other.