Deep Geometric Learning with Monotonicity Constraints for Alzheimer's
  Disease Progression
Seungwoo Jeong Wonsik Jung Junghyo Sohn Heung-Il Suk
Alzheimer's disease (AD) is a devastating neurodegenerative condition that
precedes progressive and irreversible dementia; thus, predicting its
progression over time is vital for clinical diagnosis and treatment. Numerous
studies have implemented structural magnetic resonance imaging (MRI) to model
AD progression, focusing on three integral aspects: (i) temporal variability,
(ii) incomplete observations, and (iii) temporal geometric characteristics.
However, deep learning-based approaches regarding data variability and sparsity
have yet to consider inherent geometrical properties sufficiently. The ordinary
differential equation-based geometric modeling method (ODE-RGRU) has recently
emerged as a promising strategy for modeling time-series data by intertwining a
recurrent neural network and an ODE in Riemannian space. Despite its
achievements, ODE-RGRU encounters limitations when extrapolating positive
definite symmetric metrics from incomplete samples, leading to feature reverse
occurrences that are particularly problematic, especially within the clinical
facet. Therefore, this study proposes a novel geometric learning approach that
models longitudinal MRI biomarkers and cognitive scores by combining three
modules: topological space shift, ODE-RGRU, and trajectory estimation. We have
also developed a training algorithm that integrates manifold mapping with
monotonicity constraints to reflect measurement transition irreversibility. We
verify our proposed method's efficacy by predicting clinical labels and
cognitive scores over time in regular and irregular settings. Furthermore, we
thoroughly analyze our proposed framework through an ablation study.