*4.5. Discriminant Parameter Selection*

The choice of the best parameters used to train the classifiers was performed by selecting the sets of kinematic parameters which best correlate with the UPDRS scores of subjects' performances.

The initial sets of parameters considered to characterize every single task consisted of more than ten parameters per set: they were chosen to be closely related to those features that are implicitly considered by neurologists to assess the motor performance. These initial sets could potentially include irrelevant and redundant parameters, which could hide the effects of the clinically relevant ones, reducing the predictive power of the classifiers used for the automated assessments. To avoid this, a feature selection (FS) procedure [56] is performed by the Elastic Net (EN) algorithm [57]. EN is a hybrid of Ridge regression and LASSO regularization. EN encourages a grouping effect on correlated parameters, and tends to be more conservative respect to LASSO or Ridge regression in removing correlated parameters, a process which can select incorrect data model. This capability is important when dealing with those features which are similar and tend to be moderately correlated. The EN implementation is based on Matlab scripts (lasso Matlab function). To avoid biasing the results by the different scaling, the PD parameters *p*i PD have been normalized (Equation (2)) by the corresponding average values of the HC parameters *p*i HC. Then the normalized parameters range from the value 1 (*p*i HC ) to a maximum (*p*i PD Norm MAX > 1), or to a minimum (0 < *p*i PD Norm MIN < 1), depending if the value of the specific parameter increases or decreases when the severity of the impairment increases. The parameter Number of Poor movements (PM), whose minimum value is 0, was not normalized:

$$p\_{\text{i PD}\,\text{Norm}} = p\_{\text{i PD}} / p\_{\text{i RC}\,\text{V}} \tag{2}$$
