Imputation of Missing Data in Smooth Pursuit Eye Movements Using a Self-Attention-based Deep Learning Approach

Missing data is a relevant issue in time series, especially in biomedical sequences such as those corresponding to smooth pursuit eye movements, which often contain gaps due to eye blinks and track losses, complicating the analysis and extraction of meaningful biomarkers. In this paper, a novel imputation framework is proposed using Self-Attention-based Imputation networks for time series, which leverages the power of deep learning and self-attention mechanisms to impute missing data. We further refine the imputed data using a custom made autoencoder, tailored to represent smooth pursuit eye movement sequences. The proposed approach was implemented using 5,504 sequences from 172 Parkinsonian patients and healthy controls. Results show a significant improvement in the accuracy of reconstructed eye movement sequences with respect to other state of the art techniques, substantially reducing the values for common time domain error metrics such as the mean absolute error, mean relative error, and root mean square error, while also preserving the signal's frequency domain characteristics. Moreover, it demonstrates robustness when large intervals of data are missing. This method offers an alternative solution for robustly handling missing data in time series, enhancing the reliability of smooth pursuit analysis for the screening and monitoring of neurodegenerative disorders.