## 4 Discussion
### Optimal Features  
Figure 4 highlights the dominance of specific optimal feature subsets during subject-wise leave-one-out cross-validation (LOOCV). The most frequently selected optimal three-feature subset comprises velocity-related features: Vy_pct75, Vy_std, and V_pct25. This subset also appears within the dominant nine-feature and eleven-feature configurations. Notably, Table 4 shows that Vy_std and Vy_pct75 rank among the top three features with the lowest \(p\)-values and highest absolute correlation coefficients relative to class labels. Figure 5 presents boxplots for the dominant three-feature subset, illustrating its effectiveness in distinguishing between the depressive disorder (DD) and control groups. Additional boxplots for the dominant nine- and eleven-feature subsets are provided in Appendix E. Across all selected features, handwriting velocity--whether measured along the \(x\)-axis, \(y\)-axis, or as total velocity--was consistently reduced in DD patients, reflecting a slower writing pattern. This finding aligns with previous studies that identified psychomotor retardation as a hallmark of depressive symptoms [17; 18; 23; 34]. While our machine learning model demonstrated high classification accuracy--most notably 82.5% using three velocity-based handwriting features--it is critical to interpret these results in terms of clinical relevance. The velocity-based features identified in our study (e.g., reduced average stroke speed, longer inter-stroke intervals) are likely direct, quantifiable proxies for psychomotor slowing. These features are not merely algorithmic artifacts but reflect well-documented clinical observations of motor retardation in depression. By incorporating such features into a structured digital assessment--such as a brief handwriting task on a tablet--clinicians could objectively detect psychomotor changes that might otherwise go unnoticed in standard clinical interviews. This may be particularly valuable in cases where youth struggle to articulate internal states or when symptom reporting is inconsistent [57; 58]. Thus, the handwriting-based features offer more than predictive accuracy: they reflect neurocognitive and motor-behavioral processes central to depressive pathology, paving the way for more precise, accessible, and developmentally appropriate diagnostic tools in youth mental health care. In this context, the machine learning model is not merely a technical classifier but a translational bridge between digital behavior signals and clinically actionable insights. The present findings underscore the potential of handwriting velocity as a clinically relevant digital biomarker for identifying psychomotor disturbances (i.e., psychomotor retardation) in youth with depressive disorder (DD). The observed reduction in handwriting speed among depressed adolescents provides objective evidence of a core symptom traditionally evaluated via clinical observation or subjective rating scales, thereby complementing standardized assessments. Importantly, the high classification accuracy achieved using a logistic regression model and velocity-based features suggests that this method could augment existing diagnostic practices, offering a low-cost, accessible, and scalable assessment tool for depression in youth. Integrating such digital markers into routine diagnostic frameworks may enhance diagnostic precision, particularly in cases where verbal self-report is limited or inconclusive. While traditional tools provide generalized assessments, handwriting analysis and specific kinematic parameters may correlate with features characteristic of certain subtypes, as previously reported in adult populations [16]. Furthermore, this approach aligns with the principles of precision psychiatry and can contribute to digital phenotyping [59], forming a basis for remote monitoring and early detection of depressive symptoms in community and school settings [60].