Quaternion-Based Representation for Visual Depression Detection: Enhanced Performance Through Geometric Feature Fusion

Depression remains a leading cause of global disability, yet many avoid help due to stigma, cost and limited access, highlighting the need for non-invasive, scalable screening tools. Classical approaches to visual depression detection often concatenate 3-Dimensional (3D) behavioural cues such as head pose, gaze and facial action units as independent features, neglecting their inherent spatial and rotational interdependencies. This paper proposes a novel feature representation strategy that encodes these geometric visual signals as 4-Dimensional (4D) quaternions, leveraging hypercomplex algebra to preserve 3D orientation structure and avoid gimbal lock. Using visual features from the DAIC-WOZ dataset, we transform OpenFace-derived cues into quaternion representations and train classical machine learning models without deep learning or multimodal inputs. Our best configuration, Decision Tree with quaternion-encoded head pose achieves an F1-score of 0.80 on the development set, significantly outperforming traditional 3D-concatenated baselines (e.g., Blink + Eye gaze: F1 = 0.73). On the held-out test set, eye gaze (CatBoost) generalizes best (F1=0.79), while Head pose drops to 0.42 which reveals important insights about cue stability in small-sample clinical ML. Ablation studies confirm that quaternion encoding is most effective for rotational cues like head pose, while fusing less informative signals (e.g., blinks) degrades performance. This work demonstrates that data strategic geometric representation is key to high-performance depression screening, offering a lightweight interpretable alternative to complex multimodal pipelines.