## 2 Materials and Methods
### Dataset  
The publicly available data of [10] collected gait spatiotemporal parameters and joint kinematics of the lower limbs of 142 subjects. A list of demographic and anthropometric data (such as age, gender, weight, and height) is available for each subject, and additional clinical data are provided for patients affected by each neurodegenerative disease. The composition of the dataset is illustrated in Table 1.  
The gait parameters measured are cadence (in steps per minute), speed (in meters per second), step width (in meters), stance and swing time, double support time (provided as a percentage of the gait cycle), step length (in meters), and the sagittal plane range of motion (ROM) of hip, knee, and ankle joints. All of the listed measures above are provided for the right and left limbs (except for cadence and step width by definition). For more information about data acquisition and processing, please refer to the work by [10]. Since spatial and temporal parameters, such as speed, are influenced by body size, the data needed to be normalized to achieve a better comparison. We used the Froude number [17] to normalize the speed, which is defined as follows:  
\[v^{*}=\frac{v}{\sqrt{gh}} \tag{1}\]  
where \(g\) is the gravitational acceleration, and \(h\) is the height of the subject. Moreover, spatial and temporal parameters were used to compute indexes for evaluating walking patterns. We used the walk ratio [18], given by the ratio between step length and cadence. This parameter reflects the degree of gait coordination between spatial and temporal walking aspects (i.e., step length and cadence, respectively). It has been shown that it is reproducible and does not vary over a wide range of speeds [18; 19]. Since the subjects involved in the study were asked to walk at a self-selected speed, this parameter represents a useful yet simple parameter to describe the rhythm and amplitude of walking. Also, the walk ratio was normalized with subjects' height, since the step length is related to body size. This normalization can be relevant for avoiding erroneous correlation, as shown in [20]. Figures S1 and S2 of the Supplementary Materials show that the application of the Froude number for the speed and the normalization of the step length made these metrics not correlated to subjects' height and age. To avoid redundancies in the gait features provided to the classifiers, the walk ratio replaced the step length and cadence parameters. Another parameter considered consistent for comfortable walking speed is the ratio between stance and swing times, which typically occupy around 60% and 40% of the gait cycle, respectively. A change in this ratio is usually associated with pathological gait [21]. We thus used the ratio between stance and swing time for left and right limbs, removing the stance and swing from the set of features to avoid redundancies. Among the gait parameters provided by the dataset, we decided not to use the ankle ranges of motion in our study. This choice was related to an anomalous asymmetry reported in the values of the left-side ankle range of motion among the healthy subjects, which resulted in significantly higher values than the right-limb ones. An in-depth statistical analysis is reported in Appendix A. In this work, we focused only on gait parameters for classification, intentionally excluding anthropometric and clinical data (except for subjects' height measurements, which were used for normalization purposes). This approach was intended to capture the most relevant gait-related features for classification. Additionally, since some of the employed classifiers, particularly those based on distance metrics or gradient-based optimization, are sensitive to differences in the scale of input features, we standardized each gait parameter individually using the z-score.