Depression severity prediction using multidimensional eye and head features: a Lanczos-based quaternion singular spectrum analysis approach

Depression is a pervasive mental health disorder affecting millions worldwide. There is an urgent need for objective automated tools for early detection and severity prediction. Current automated approaches often fail to adequately address temporal dependencies between data channels and remain vulnerable to noise interference. Notably, eye and head dynamics - among the most accessible non-verbal behavioral biomarkers for depression - remain understudied despite their suitability for collection via consumer smart eyewear in home environments. This paper presents a novel Lanczos-based quaternion-based Singular Spectrum Analysis approach for fast and robust feature extraction from eye-head movement patterns. The method employs quaternion signal processing to extract features holistically from multidimensional eye and head movement signals while preserving their intrinsic spatiotemporal relationships. These features remove the interference from noise and outlier, and enable accurate machine learning-based depression assessment. Validated on the benchmark Distress Analysis Interview Corpus (DAIC) dataset and the extended DAIC (E-DAIC) dataset, the proposed method outperforms conventional visual modality-based approaches in depression severity prediction task. For the DAIC dataset, the system achieved a root mean square error (RMSE) of 5.26, and a mean absolute error (MAE) of 4.08 on the development set. On the testing set, the system achieved an RMSE of 4.74, and an MAE of 3.83. Furthermore, for the E-DAIC dataset, the system achieved an RMSE of 4.26, and an MAE of 3.53 on the development set. Detailed analysis, including various ablation studies, further demonstrates the method's effectiveness and highlights promising applications of wearable sensor data in mental health diagnostics.