Kernel Quaternion Principal Component Analysis of Eye and Head Dynamics for Depression Severity Prediction

Depression is a global mental health challenge that necessitates accurate and timely diagnosis. Studies have shown that features extracted from eye dynamics and head movements constitute a non-invasive and real-time means of monitoring behavioral biomarkers associated with depression. However, representing and analyzing these high-dimensional, time-varying signals for medical diagnosis poses significant challenges, including computational inefficiency, loss of temporal information, and the inability to capture complex interrelations between movement channels. This paper proposes a novel algorithm that leverages kernel quaternion principal component analysis to extract features from eye and head dynamics, represented as quaternion time series signals, preserving channel-wise interrelations and temporal information. Additionally, a model-based quaternion interpolation method is introduced to address class imbalance by augmenting depression samples. The proposed approach is evaluated on a benchmark depression dataset, demonstrating superior accuracy in predicting depression severity with a root mean square error (RMSE) of 4.84 and a mean absolute error (MAE) of 3.88. When applied to the augmented dataset, the algorithm achieves further improvement, with an RMSE of 4.48 and an MAE of 3.53. These results outperform previous methods based solely on eye and head dynamics, highlighting the potential of quaternion-based signal processing in advancing mental health diagnostics. The proposed framework is particularly promising for integration into consumer systems for healthcare and wellbeing, such as smart eyewear, offering a practical and accessible solution for the early detection and intervention of depression by equipping individuals with tools to manage their mental wellbeing in everyday life.