A self-supervised deep Riemannian representation to classify parkinsonian fixational patterns

Parkinson's disease (PD) is the second most prevalent neurodegenerative disorder, and it remains incurable. Currently there is no definitive biomarker for detecting PD, measuring its severity, or monitoring of treatments. Recently, oculomotor fixation abnormalities have emerged as a sensitive biomarker to discriminate Parkinsonian patterns from a control population, even at early stages. For oculomotor analysis, current experimental setups use invasive and restrictive capture protocols that limit the transfer in clinical routine. Alternatively, computational approaches to support the PD diagnosis are strictly based on supervised strategies, depending of large labeled data, and introducing an inherent expert-bias. This work proposes a self-supervised architecture based on Riemannian deep representation to learn oculomotor fixation patterns from compact descriptors. Firstly, deep convolutional features are recovered from oculomotor fixation video slices, and then encoded in compact symmetric positive matrices (SPD) to summarize second-order relationships. Each SPD input matrix is projected onto a Riemannian encoder until obtain a SPD embedding. Then, a Riemannian decoder reconstructs SPD matrices while preserving the geometrical manifold structure. The proposed architecture successfully recovers geometric patterns in the embeddings without any label diagnosis supervision, and demonstrates the capability to be discriminative regarding PD patterns. In a retrospective study involving 13 healthy adults and 13 patients diagnosed with PD, the proposed Riemannian representation achieved an average accuracy of 95.6% and an AUC of 99% during a binary classification task using a Support Vector Machine.