## 4 Discussion  
To the best of our knowledge, except for our pilot work [20], there are no prior studies which integrate FD into a handwriting parameterization for quantitative PD dysgraphia analysis. Therefore, the results published in this paper are exploratory in nature. \begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Feature Set** & **MAE** & **RMSE** & **EER [\%]** & **Feat** \\ \hline \multicolumn{5}{c}{UPDRS V} \\ \hline conventional on-surface & \(0.59\pm 0.29\) & \(0.71\pm 0.41\) & \(13.82\pm 6.71\) & \(1\) \\ conventional in-air & \(0.60\pm 0.30\) & \(0.72\pm 0.42\) & \(14.01\pm 6.98\) & \(1\) \\ conventional together & \(0.60\pm 0.31\) & \(0.73\pm 0.42\) & \(14.05\pm 6.90\) & \(1\) \\ FD on-surface & \(0.60\pm 0.32\) & \(0.65\pm 0.45\) & \(\mathbf{12.51\pm 7.55}\) & \(1\) \\ FD in-air & \(0.60\pm 0.33\) & \(0.68\pm 0.43\) & \(13.49\pm 7.29\) & \(1\) \\ FD together & \(0.60\pm 0.34\) & \(0.66\pm 0.45\) & \(13.06\pm 7.55\) & \(2\) \\ all on-surface & \(0.60\pm 0.35\) & \(0.65\pm 0.45\) & \(\mathbf{12.51\pm 7.55}\) & \(1\) \\ all in-air & \(0.60\pm 0.36\) & \(0.71\pm 0.43\) & \(13.72\pm 7.36\) & \(1\) \\ all together & \(0.60\pm 0.37\) & \(0.66\pm 0.45\) & \(13.06\pm 7.55\) & \(2\) \\ \hline \multicolumn{5}{c}{PD duration} \\ \hline conventional on-surface & \(4.29\pm 0.94\) & \(5.03\pm 1.09\) & \(24.52\pm 5.39\) & \(18\) \\ conventional in-air & \(4.91\pm 1.38\) & \(5.56\pm 1.50\) & \(28.03\pm 7.85\) & \(16\) \\ conventional together & \(4.14\pm 1.32\) & \(4.85\pm 1.52\) & \(\mathbf{23.64\pm 7.55}\) & \(16\) \\ FD on-surface & \(4.45\pm 0.66\) & \(5.06\pm 0.85\) & \(25.40\pm 3.75\) & \(14\) \\ FD in-air & \(4.79\pm 0.73\) & \(5.48\pm 0.72\) & \(27.36\pm 4.20\) & \(19\) \\ FD together & \(4.55\pm 0.68\) & \(5.32\pm 0.78\) & \(26.00\pm 3.88\) & \(21\) \\ all on-surface & \(4.48\pm 0.86\) & \(5.12\pm 0.96\) & \(25.62\pm 4.92\) & \(16\) (\(12\) F, \(4\) C) \\ all in-air & \(4.95\pm 1.18\) & \(5.59\pm 1.17\) & \(28.30\pm 6.75\) & \(17\) (\(13\) F, \(4\) C) \\ all together & \(4.70\pm 1.10\) & \(5.45\pm 1.23\) & \(26.82\pm 6.30\) & \(17\) (\(12\) F, \(6\) C) \\ \hline \end{tabular}
\end{table} 
Table 7: Results of regression analysis for clinical data. In comparison with the conventional kinematic features, FD-based ones correlate more significantly with the clinical characteristics (UPDRS V and PD duration). We observed especially strong correlations for handwriting tasks based on the periodic repetition of specific movements (Archimedean spiral; repetitive letter \(l\), syllable \(le\), or word \(les\)). Although the levels of significance based on the conventional handwriting parameters are lower, similar handwriting tasks are involved in the most significant results. We hypothesize that this is due to their ability to highlight or better quantify the cardinal motor symptoms of PD. For example, the most significant relationship between handwriting performance and PD duration was identified in acceleration extracted from the Archimedean spiral. Rigidity combined with tremor and/or bradykinesia makes a PD patient's handwriting/drawing less fluent (increased changes in velocity and higher acceleration). This is highlighted in a task such as the spiral, where the proper coordination of the fingers, wrist, and arm is required. Generally, the observed problems with coordination are in line with the work of [PERSON] et al. [51] and [PERSON] et al. [52]. To better illustrate these manifestations, Figure 3 plots the velocity profiles of repetitive loops for a healthy control and a PD patient. As can be seen, the patient introduced more changes in velocity, and their drawing became much more non-fluent. To summarize these findings, FD features in combination with properly selected tasks provide a stronger relationship with the severity and progress of PD. On the other hand, in terms of binary classification, the conventional parameters provided the best results. The classification performance is remarkable: \(\text{ACC}=97.74\%\), \(\text{SEN}=95.50\%\), and \(\text{SPE}=100\%\).